The two clubs are believed to have agreed a fee in the region of £15m for the Austrian who is expected to complete his move in the next few days.
Wimmer had previously attracted interest from West Brom and Crystal Palace but it is Stoke who appear to have won the race for his signature.
The Austrian international made just four Premier League starts last season and has only made 15 league appearances in total since his move from Koln in 2015.
Wimmer has yet to play for Mauricio Pochettino's side this season ans slipped further down the pecking order at Spurs following the arrival of Davinson Sanchez from Ajax.
Should all go to plan, Wimmer will become Mark Hughes' seventh major signing of the summer and provide further defensive reinforcements to a side that has already brought in Kurt Zouma, Bruno Martins-Indi and Josh Tymon during the transfer window.