Di Santo has signed a three-year contract with the Bundesliga club and will vie with Nils Peterson, Marko Arnautovic and Joseph Akpala to start in attack.
The Argentina international made 97 appearances for Wigan during his three-year stay at the DW Stadium, scoring 13 goals.
However, after the club were relegated from the Premier League last season he left at the end of his contract.
Werder are expected to unveil Di Santo on Thursday, and the 24-year-old is looking forward to his new challenge.
"Werder has a very good reputation and the Bundesliga is an attractive league," he told the club's official website. "I want to show here what I can do."
Thomas Eichin, sporting director at Bremen, believes Di Santo is just what his side have been looking for to help them improve on their 14th-place finish last season.
"We were looking for a robust striker who already has experience in a big league," Eichin said. "We are sure that in Franco Di Santo we have found a good solution.
"He has experience, but he also has enough development potential to make a big step forward. He wants [to go to] the World Cup with Argentina in 2014 and we would be delighted he reached the goal."
Di Santo was part of the Wigan squad that won the FA Cup last season, the club's first ever major trophy.