The Senegal forward joined Hoffenheim in August 2007 and helped them in their rise to Germany's top flight.
But a move away seemed likely after Ba refused to travel with Hoffenheim to their winter training camp in Spain amid interest from West Ham United.
He was threatened with legal action by the club's general manager, although Ba suggested in a statement on his own website that Hoffenheim had gone back on a promise to let him move to England.
I'm so excited about the chance to get Demba Ba. This is a player I have rated for a long time
stokeymad
"I regret the situation and I suffer from it," Ba said on 6 January. "The club gave me a green light to leave under certain conditions which have been met. I hope that the promises will be fulfilled."
The Potters have a number of attacking options already at the club and it is likely that manager Tony Pulis will allow one of his strikers to leave the Britannia Stadium if, as expected, Ba completes his transfer.
Former Chelsea and Barcelona forward Eidur Gudjohnsen is yet to start a match since joining Stoke in August, while Tuncay posted a video of some of his favourite goals on social networking site Facebook, which some media outlets believe was an attempt to secure a move elsewhere after growing frustrated with his lack of opportunities at the club.
Source: BBC Sport
Source: BBC Sport