Former Manchester United striker Diouf, who has been a long-term target of the Potters, will join up with his new team-mates on July 1 when his contract at Hannover expires.
He has signed a four-year contract while central defender Teixeira has joined for an undisclosed fee from Slovakian side Banska Bystrica on a three-year deal.
The 21-year-old was born in Brazil but is a current member of the Slovak Under-21 squad.
Chief executive Tony Scholes told stokecityfc.com: "It's no secret that Mame is someone we have been looking to bring to the club for some time.
"Mark Hughes has wanted to sign Mame since he took over as manager last year. We tried to get him last summer and made another attempt in January, so we're naturally delighted to have finally secured his services.
"He has been a tremendous success in Germany as his record underlines and he is keen to return to England and make an impact in the Premier League.
"We have been following Dionatan's progress for some time and we're delighted to have secured his services because there's no doubt he's a talented player with a great deal of potential."
- Sports & Recreation
- Phil Bardsley
- Steve Sidwell