His announcement was greeted with applause from all sides of the legislature, and a standing ovation from opposition benches.
Mr Bercow is seen as a somewhat unpopular figure among many Brexiteers because he has on a number of occasions sided with Remainers.
The protesting Parliamentarians crowded around John Bercow chanting and holding signs that read "Silenced" as the prorogation ceremony began on Monday night.
"Don't tell me, young man. what I can and can't say", he bellowed at one heckler on Monday. He likes to think of himself as a reforming Speaker, yet he's been dogged by scandals and given up any pretence he is impartial.
But historic parliamentary convention states that he will generally be unopposed by the major political parties, who will not field a candidate in the Speaker's constituency.
Ms Harman, who was a prominent Remain campaigner in the European Union referendum, said she would be able stand back from political issues if she became Speaker.
As Conservative MPs heckled him, Bercow replied: "I could not give a flying flamingo what your view is!"
While she said it was "not funny" and that she had protested when she first heard it, Neill stopped her from speaking further and later tweeted that he had been "appalled" that she should say such a thing live on TV.
"At the 2017 election, I promised my wife and children that it would be my last", Mr Bercow told the House of Commons as his wife Sally looked on from the gallery.
"This is a pledge that I intend to keep".
Mr Bercow said if he had waited to stand down after the next election, newly-elected MPs would not be "informed" enough to make the right choice.
Labour leader Jeremy Corbyn praised Bercow for being a "superb" speaker.
Several MPs were also involved in an altercation near the Speaker's chair as they attempted to prevent him leaving his seat and attending the House of Lords, the next step in the formalities required for the suspension of Parliament, the BBC reported.
In recent months he came under fire for a series of controversial rulings in the chamber which were widely considered to favour Remain supporters.
In January, he came under pressure to resign after he was found to have a "Bollocks to Brexit" sticker in his auto window.