The former Strasbourg ace had agreed a move to the Premier League new-boys, but the deal fell through over work-permit problems.
Stuttgart then stole in to lure the 22-year-old to Germany before the close of the transfer window on Tuesday.
Bah admits he is happy to have made the move to Germany, but revealed he hopes to play in the Premier League some time in the future.
"I heard Blackpool were very interested," Bah told skysports.com.
"I am a Stuttgart player now and I want to give my best to my new club and prove myself in one of the top leagues in all of the world.
"It is a dream come true for me, players such as Klinsmann played for this club.
"It is a big club here so if I can play here week in, week out I can show to all big clubs my value.
"I love the Premier League and maybe one day I will be there to play, all good players dream about it."