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Mr Bercow, who faced a no-confidence motion from MPs earlier this year, was elected unopposed and promised to be a "tested Speaker" in "testing times".
Congratulating him, Prime Minister Theresa May - who lost her Commons majority in the election - joked: "At least someone got a landslide."
Jeremy Corbyn got a standing ovation from Labour MPs as he took his seat.
Mr Corbyn - who defied the pollsters and gained 30 seats on Thursday - congratulated Mrs May on returning as prime minister, adding: "I am sure she will agree with me that democracy is a wonderful thing and can bring up some very unexpected results."
Before the Speaker election, the MPs were formally summoned to the House of Lords - with Theresa May and Jeremy Corbyn walking side by side - before returning to the Commons.
Conservative MP Ken Clarke, the Father of the House, chaired proceedings as Mr Bercow spoke from the backbenches, saying he would be "honoured to serve" in the Speaker's chair again.
"I will strive to ensure that all parts of the House are heard fully and fairly," he said, promising to champion the right of backbenchers to hold the government to account.
He added: "We appear to be heading for testing times. I offer myself to the House as a tested speaker."
The election of the Speaker was the only business scheduled for the day, and there is uncertainty over the date of the Queen's Speech which will launch the next Parliamentary session.