Former Manchester United and Blackburn Rovers forward Diouf, a long-time Stoke target, has penned a four-year deal at the Britannia Stadium and will join his new club on July 1 when his contract at Hannover expires.
In 57 league appearances for Hannover, the Senegal international scored 25 goals.
Brazil-born defender Teixeira joins for an undisclosed fee from Slovak Super Liga outfit Banska Bystrica and has agreed a three-year deal.
The capture of Diouf brings a positive end to Stoke's lengthy interest in the 26-year-old.
Stoke chief executive Tony Scholes told the club's official website: "It is 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 make an impact in the Premier League.
"We're pleased to be able to give him the platform to hopefully achieve that ambition."
Teixeira, who turns 22 next month, joins Diouf, Steve Sidwell and Phil Bardsley as Stoke's close-season signings to date.
Scholes added: "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."
