The Denmark international made 71 league appearances for Hoffenheim after joining from Brondby in 2010.
However, the 22-year-old has slipped down the pecking order at the Rhein Neckar Arena this term and has featured in just six Bundesliga games.
Vestergaard moves to Bremen on a deal that runs until June 2018 and will attempt to shore up a defence that has conceded 39 league goals this term, the highest amount in the Bundesliga.
"We want to develop the squad," said Bremen head coach Viktor Skripnik.
"He [Vestergaard] is strong in the centre, has a physical presence and is tactically very aware."
Bremen sit in the Bundesliga relegation play-off spot and return to action following the mid-season break at home to Hertha Berlin on Sunday.
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