Di Santo, 24, has signed a three-year contract with the Bundesliga club who will unveil him on Thursday.
Bremen general manager Thomas Eichin describes Di Santo as a "robust striker" with experience in a major league and "still enough potential for development."
Werder director of sport Thomas Eichin confirmed the frontman passed his
medical at a Bremen clinic on Tuesday.
Eichin told the club's official website: "We had been in the hunt for a robust striker with experience in a big league.
"We are very confident that we have found a good solution in Franco Di Santo.
"He is experienced but still possesses enough potential for development in order to make a great leap forwards.
"He wants to make it to the 2014 World Cup with Argentina and we would be very happy if he gained the necessary attention playing in Bremen for him to achieve that goal."
Di Santo said: "Werder have a very good name and the Bundesliga is a very attractive league. I want to show what I am capable of here."
Di Santo played for Chilean side Audax Italiano before joining Chelsea in 2008.
He spent a year on loan at Blackburn Rovers before joining Wigan in 2010.