Sky Sports says Wimmer, 24, has agreed to the move to the bet365 Stadium and will have a medical in the coming days.
The Austria international had been made surplus to requirements by Spurs boss Mauricio Pochettino following the signing of Davinson Sanchez from Ajax in a reported club-record £42m deal last week.
Wimmer is set to become the seventh summer arrival at Stoke following Kurt Zouma, Darren Fletcher, Josh Tymon, Eric Maxim Choupo-Moting, Bruno Martins Indi and Jese Rodriguez.
However, the 24-year-old will only be the third player Stoke will have spent money on this summer, with Zouma and Jese arriving on loan and Fletcher and Choupo-Moting signed on free transfers.
Potters chairman Peter Coates defended the club's spending in the transfer window earlier this month and hinted that more players could be brought in.
"These players become very expensive," Coates told BBC Radio Stoke on 17 August. "The media urge them on, managers urge them on, and coaches urge them on but somebody has to pay the bill. We can pay big wages and big loan fees.
"As for further signings, it depends whether opportunities arise that suit us. One or two situations we're still looking at and we'll have to see how they develop between now and the transfer window closing."
Wimmer joined Tottenham from Cologne in 2015, but made only 15 Premier League appearances for the north London club in two seasons. He has four years left on his Spurs contract.
Pochettino said he expected to make three new signings before the transfer window shuts on 31 August.
"We are working hard to try and add more quality to the squad. There are many rumours and we are working hard," the Argentine was quoted as saying by the London Evening Standard after Tottenham's 1-1 draw with Burnley.