U.S. President Ronald Reagan (1911-2004) described, in a speech on June 8, 1982, before the British Parliament, “the march of freedom and democracy which will leave Marxism-Leninism on the ash-heap of history as it has left other tyrannies which stifle the freedom and muzzle the self-expression of the people.” It’s often said (incorrectly) that Leon Trotsky (1879-1940) coined the term “ash heap of history” in 1917. The term—and other, similar terms—means that something will be discarded (like trash) and will not exist in the future.
 
“Dustbin of history” has been cited in print since at least 1870. “Rubbish heap of history” has also been cited in print since 1870. “Ash-heap of history” has been used since 1898. “Scrap heap of history” has been used since 1900. “Waste heap of (human) history” has been used since 1899. “Junk heap of history” has been used since 1911. “Garbage heap of history” has been used since 1922. There are probably other forms of the expression, but it’s clear that Trotsky could not have coined it in 1917.
 
 
Wikipedia: Ash heap of history
The ash heap of history (or often garbage heap of history or dustbin of history) is a figurative place to where objects such as persons, events, artifacts, ideologies, etc. are relegated when they are forgotten or marginalized in history.
 
The expression—or something like it—was coined by Leon Trotsky in response to the Mensheviks walking out of the Second Congress of Soviets, on October 25, 1917, thereby enabling the Bolsheviks to establish their dominance. Trotsky declared: “Go out where you belong—into the ash heap of history.” A more dramatic version of this event puts Trotsky as saying: “‘You are pitiful, isolated individuals! You are bankrupts. Your role is played out. Go where you belong from now on—into the dustbin of history!’”
 
It has since been used in both the direct and the ironic sense in political and nonpolitical contexts.
 
Later, it was most notably used by Ronald Reagan in a speech to the British House of Commons on June 8, 1982. This speech is a lasting hallmark of the Reagan presidency, but not as memorable as the “Evil empire” speech of March 8, 1983, with which it is often confused. Reagan’s speechwriter chose the expression deliberately because of its prior context. His exact phrase was: “... freedom and democracy will leave Marxism and Leninism on the ash heap of history.”
         
Newspapers.com
20 March 1870, New Orleans (LA) Times, pg. 2, col. 2:
... the rust is at work, and not many years will pass before the dust bin of history will enshrine it, by general consent of a people, with higher, nobler, and more fraternal aims than their predecessors.
 
September 1870, Macmillan’s Magazine (Cambridge, UK), “The Duel of Nations,” pg. 330:
The three unpopular ruling houses that had divided the northern half of Germany against Prussia were swept away into the dustbin of history, and Hanover, Cassel, and Nassau made part of the enlarged kingdom of the Hohenzollern.
   
Newspapers.com
8 September 1870, New-York (NY) Times, “The French Army and the Republic” (editorial), pg. 4, col. 4:
NAPOLEON is a prisoner of war; the Empire has been swept into the rubbish heap of history.
   
Google Books
My time, and what I’ve done with it:
An autobiography
By Sir Francis Cowley Burnand
London: Macmillan
1874
Pg. 266:
It is thus that ignorant prejudices are fostered, and how few of us in after-fife have the time, or the will, to sift the rubbish of the dustbin of History on the chance of discovering the diamond of Truth.
 
20 July 1893, The Independent (London), pg. 53, col. 2: 
It deals with the recent work of Professor Ramsay, who also writes an article in this number on the same subject, and claims that the great scholar has “brushed aside into the dustbin of history” some of the fallacies which have too long flourished as to the relation of the Roman government to the early Christians.
 
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September 1898, The Arena, “The Republic and the Empire” by John Clark Ridpath, pg. 359:   
Has representative government become a thing so poor and mean as to be cast out on the fuliginous ash-heap of history, to fester in the sun, and. to have its remaining substance sucked up by the bluebottles of a parvenu nobility?
   
Newspapers.com
13 February 1899, The Arkansas Democrat (Little Rock, AK), “The Measure of Man,” pg. 7, col. 2:
“His work is not wholly lost. It does not go simply to swell the mental and moral waste heap of human history.”
 
16 August 1900, Columbus (GA) Enquirer-Sun, “Speakers Are All for Bryan,” pg. 1, col. 4:
Thank God, the people may yet relegate it to the scrap heap of history, stamped with the seal of their disapproval.
 
Google Books
A critical history of the evolution of trinitarianism, and its outcome in the new Christology
By Levi L. Paine
New York, NY: Houghton, Mifflin and Company
1900
Pg. 235:
It is indeed pathetic to cast the eye over them and reflect how little that is vital and influential remains of the mass of these works which are already finding their own place in the dust-heap of history.
     
Google Books
Democracy and the organization of political parties
By M. Ostrogorski, translated from the French by Frederick Clarke
New York, NY: Macmillan Co.
1902
Pg. LVI:
The miscellaneous facts which hitherto have been disdainfully thrown into the rubbish-heap of history and of the political news of the day have enabled me to rise step by step to the highest generalizations of political speculation and of the political art.
       
Google Books
November 1906, Library Bulletin (Iowa Masonic Library, Cedar Rapids, IA) , pg. 95:
The waste heap of history is piled with broken systems which could not adjust themselves to changed conditions, or failed to answer to their pretensions when the test was applied, or neglected the opportunities which fate presented.
 
26 December 1909, Trenton (NJ) Evening Times, “Discovery of North Pole; Progress of Aviation,” pg.  9:
WHEN all the other happenings of 1908 shall have passed into the dustbin of history, that year will be remembered as the one in which men first lifted the veil of mystery surrounding the frigid northern extremity of the earth’s axis.
 
6 February 1911, Jersey Journal (NJ), “How Women Vote in Boston,” pg. 10, col. 6:
A hasty clutch at one’s whole scrap heap of history brought up these shining examples and metaphorically waving them in the face of the stolid presiding policemen and the casually interested men who were conducting the voting process, one entered the little building, says a writer in the Christian Science Monitor.
 
Newspapers.com
25 May 1911. Marion (KS) Record, “Current Comment” by E. W. Hoch, pg. 5, col. 4:
Dueling among men is a thing of the past and dueling among nations should find an early place in the scrap-pile and junk heap of history.
 
18 October 1913, Belleville (IL) News Democrat, “Ponderous Personage: Nebuchadnezzar” by George Fitch, pg. 4:
He conquered Egypt and won great victories at Carchemish, Tyre and other places long ago gone onto the scrap heap of history.
   
26 December 1916, Oregonian (Portland, OR), “Old 1916 Totters To Hilarious End,” pg. 13:
Poor old withered, bewihiskered 1916! He’s on his last pins. He has started hobbling down his final week on earth, a bent, tottering, hopeless old stiff. The tingle of the final paroxysm which will sweep him into the junk heap of history already is felt in his weak and wavering legs.
   
20 June 1918, Seattle (WA) Daily Times, “Peace Impossible Till Hun Military Machine Is Smashed, They Say,” pg. 8:
“UNTIL the German military machine is smashed beyond hope of rehabilitation and consigned to the scrap heap of history,”  there can be no lasting world peace.”
     
Newspapers.com
13 March 1922, The Leader (Regina, Saskatchewan), “New Psychology to Combat War Needed,” pg. 3, col. 4:
Its historical justification has vanished, and it, along with its state and institutions must be swept into the garbage heap of history.
 
15 May 1931, Lethbridge (Alberta, Canada) Herald, “The Story of Modern Russia”  by Maurice Hindus, pg. 9, col. 2:
You are fit only for the garbage heap of history.
       
1 July 1945, Chicago (IL) Sun, “Humbleness of Father Smith And Man’s Eternal Struggle” reviewed by Jack Conroy, Book Week, pg. 4, col. 1:
His “Luckpenny” was a frank novel about the Civil War in Spain, and was published when El Caudillo Franco was in much better odor with comfortable conservatives than now, when his two principle cronies, Der Fuehrer and Il Duce, have been relegated ignominiously to the trash heap of history.
   
Address to Members of the British Parliament (President Ronald Reagan)
June 8, 1982
(...)
I have discussed on other occasions, including my address on May 9th, the elements of Western policies toward the Soviet Union to safeguard our interests and protect the peace. What I am describing now is a plan and a hope for the long term—the march of freedom and democracy which will leave Marxism-Leninism on the ash-heap of history as it has left other tyrannies which stifle the freedom and muzzle the self-expression of the people.
 
New York (NY) Times
A Reagan Antecedent In Revolution
Published: June 30, 1985
To the Editor:
(...)
’‘The ash heap of history’’ is a phrase of which Mr. Reagan is fond. He told the British Parliament on June 8, 1982, that ‘‘freedom and democracy will leave Marx and Lenin on the ash heap of history.’’
 
Mr. Reagan’s words have impeccable revolutionary credentials. They were first used by Leon Trotsky on Oct. 25, 1917, in the Petrograd Soviet in proclaiming the Bolshevik Revolution. To his opponents Trotsky thundered: ‘‘You are miserable bankrupts, your role is played out: Go where you belong - to the ash heap of history.’’
HARRISON E. SALISBURY
Taconic, Conn., June 24, 1985