The teenage midfielder moves to the Weserstadion after struggling to break into Roger Schmidt's first team.
Having only made six league appearances this season, two of them starts, the 18-year-old has been sent out on loan to gain more first team experience.
"Levin's qualities are exceptional," said Leverkusen sporting director Rudi Voller. "What Levin needs now is match practice at the highest level.
"Bremen can offer him more of this than we currently can in Leverkusen, where the competition is much greater in his position."
For Viktor Skpinik's side the signing could provide a much-needed boost after the mid-season break, with the club languishing in 16th position after 17 matches.
Bremen sporting director Thomas Gauge is looking forward to seeing the youngster in action, and says the loan move benefits all parties.
"With Levin we have got one of the most sought-after talent in the Bundesliga," he said. "I am sure that this change is profitable for all parties.
"We gain an added option with great quality and Levin has a great chance to gain match practice.
"It is exactly the type of transfer that will help us."
