Reis has signed a contract until 2029, according to reports, with no transfer fee involved beyond performance-related bonuses and a sell-on percentage due to Brugge, who paid around €6m to sign him from Hamburg only last year.
The Belgian champions had informed the 26-year-old he had no sporting future at the club after he made just one appearance since mid-January.
Werder Bremen head of professional football Peter Niemeyer welcomed the signing.
"We are happy that we were able to reach an agreement with Ludo," he said. "We had very good talks with him. The way he plays football fits our desired role profile very well and he will expand our options in midfield."
Head coach Daniel Thioune highlighted Reis's versatility: "He is very strong physically in terms of running, wins a lot of balls and carries a certain goal threat.
"He is a technically well-trained midfielder whose strengths lie in the number six or number eight positions and who will help us with his quality."
Reis, who holds both Dutch and Slovakian citizenship, began his career in Barcelona's academy before spells at Groningen and Osnabrück led him to Hamburg, where he made 129 appearances across four seasons, scoring 20 goals and helping the club win promotion back to the Bundesliga last year before leaving for Brugge.
He returns to Germany with Hamburg's fiercest rivals, addressing a central midfield vacancy left by Romano Schmid's departure to Frosinone. He will wear the number 15 shirt and was set to be officially presented to supporters at Werder's fan day on Saturday, when the club face French top-flight side Auxerre in a friendly at the Weserstadion.
Reis's spell at Brugge never got going after a promising start to his career in Belgium: he made just 12 appearances across all competitions for the Belgian champions following his move last summer, with his last competitive outing coming in mid-January before he was frozen out of the squad entirely.
The switch to Bremen gives him a fresh opportunity to rebuild his career back in familiar surroundings, with Werder hopeful he can quickly recapture the consistent form that made him such an important figure during Hamburg's promotion campaign.