An statement was released on the club's official website informing that both players will move to the Rhein-Neckar-Arena in the summer.
Wiese, whose current deal with Bremen expires in the summer, had previously revealed that newly-crowned La Liga champions Real Madrid were interested in his services.
"There is some truth in that Real Madrid want to sign me," Wiese had told the Kreiszeitung. "There was contact between the club and my agent."
Apart from Real, AC Milan, Inter Milan, Juventus and Tottenham were also reportedly keen on the 30-year-old, although it has now been confirmed he will continue to ply his trade in the Bundesliga, much to the delight of Hoffenheim coach Markus Babbel.
"We couldn't pass up on the opportunity to sign such an experienced and successful goalkeeper," Babbel said. "We are very pleased that it's now a done deal.
"Tim Wiese has represented Germany at senior level, and that says it all. I'm convinced that he will play a key role in our ambitions."
The Germany international will be joined by striker Derdiyok, who has had to play second fiddle to Stefan Kiessling at Leverkusen for much of the season.
"Derdiyok is a very complete attacker, who will fit in very well in our team," Babbel said of the Swiss international.
"I am very happy that we managed to convince him to join us."
The 23-year-old moved to the BayArena from Basel in 2009, and represented Switzerland at the 2010 FIFA World Cup.