Walters, 33, has signed a two-year deal after spending seven years with the Potters, scoring 62 goals in 269 appearances.
He becomes Burnley's second summer signing after full-back Charlie Taylor joined from Championship side Leeds.
Walters' move means the Clarets now have five Republic of Ireland internationals in their squad.
He joins defenders Stephen Ward and Kevin Long, and midfielders Jeff Hendrick and Robbie Brady at Turf Moor.
Clarets striker Andre Gray, who has reportedly rejected a new contract, has been linked with a £15m move to fellow Premier League side West Ham.
Find all the latest football transfers on our dedicated page.

The settlement was reached in a compensation claim against the Northern Health and Social Care Trust.
The child, who cannot be identified, suffered hypoxia due to a delay in her delivery at Antrim Area Hospital in 2007.
It resulted in a series of complex health issues.
These included severe cerebral palsy and complex epilepsy.
Her parents sued the trust, claiming medical negligence.
The case had been due to run as a five-day trial at the High Court in Belfast earlier this month.
However, full liability was admitted a week before the listed hearing date.
The figure of £5.3m covers damages and the costs of past and future care for the child.

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The Foxes beat Hull 3-1 on Saturday and have won both of their games under Shakespeare since Ranieri's sacking.
"Suddenly he wants to be a manager. It doesn't sit that comfortably with me," Keown said on Match of the Day.
"If you're assistant manager to Ranieri and he's walked, why is it you suddenly want to be the manager?"
Shakespeare, 53, has never managed full-time and was brought to Leicester by Ranieri's predecessor Nigel Pearson.
He says he expects to speak with the Leicester hierarchy about his future next week.
"You have personal ambition, but I think it's almost out of order that he wants to jump in for that job," said Keown.
"Surely they'll go for a manager who is bigger with more experience."
Former Liverpool midfielder Danny Murphy added: "While Craig Shakespeare is winning, leave him in charge. Why change? Let him carry on."
Speaking after his side moved five points clear of the relegation zone, Shakespeare said: "My remit was to win these two games and that's what we've done," he said.
"The owners will make a decision for the good of the club and until I talk to them I don't know what that will be. But as I have said previously, I'm comfortable with that.
"I can't control it and there's no point worrying about it."
Leicester had not scored a league goal in 2017 until Shakespeare took charge, but have now scored six in two games - twice as many Premier League goals as they did in their last 10 matches under Ranieri.
Shakespeare has never managed a club before but has a long association with the Foxes.
The Englishman was assistant manager to Nigel Pearson for two years from 2008, following Pearson to Hull in 2010 before they both returned to Leicester a year later.
Following Pearson's sacking in 2015, Shakespeare remained at the club as Ranieri's assistant.
Leicester are believed to have spoken to a number of potential candidates to replace Ranieri, but could also consider giving Shakespeare the job until the end of the season.
The Foxes have held informal discussions with former England boss Roy Hodgson.
The 69-year-old has been out of work since leaving the international set-up after the Three Lions lost to Iceland at Euro 2016.
Pearson, who saved Leicester from relegation in 2014-15, has also been linked with a return.
Burnley have signed Republic of Ireland striker Jon Walters from Stoke City for a fee that could reach £3m.
[NEXT_CONCEPT]
An eight-year-old girl from County Antrim who was left profoundly disabled after being starved of oxygen at birth is to receive £5.3m.
[NEXT_CONCEPT]
Leicester City caretaker boss Craig Shakespeare is "out of order" for wanting to replace Claudio Ranieri, says ex-Arsenal defender Martin Keown.