The 24-year-old left Wigan at the end of last season and has linked up with Bremen on a three-year deal. He could make his debut at the Weser Stadion against Augsburg on Saturday.
He hopes the move to the Bundesliga will revive his chances of representing Argentina at the World Cup in Brazil next summer, once he gets to grips with his new surroundings.
"I'm incredibly pleased to be here and can promise that every fan will soon see what Franco Di Santo can do," he said.
"They can count on me and I will pay back their faith with good performances. I personally, but also the team, need time.
"Therefore, I hope that the fans will have a bit of patience if things don't work out immediately."
Once he does hit form, Di Santo hopes not only the Bundesliga will get to see it.
"I'm sure that the way back into the national team can only come from playing well for my club," he added on Werder's website.
"Only if I play a good season here will I have a chance of being involved in Brazil.
"There are world-class players in every position for the Argentina national team and it's hard to play, but I've had a few chances in the past and I hope to get more in future."
Di Santo joins a Bremen side which struggled to a last-gasp win over Eintracht Braunschweig last weekend.
Opponents Augsburg were beaten more convincingly, on the other hand, and they will be desperate to bounce back from a 4-0 reverse to Borussia Dortmund.
They have also invested in a new Argentinian forward, with Raul Bobadilla arriving from Swiss champions Basle.
"It's great that this transfer has worked out," said Augsburg coach Markus Weinzierl. "We can build on another alternative who can help in our attack with Raul."
Bobadilla brings with him the experience of 59 Bundesliga appearances for Borussia Monchengladbach between 2009 and 2012, a spell in which he scored eight goals and set up a further 11.