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The Dutchman, who initially broke through United's academy ranks in 2016, made 30 competitive first-team appearances in all for the club, having struggled for regular minutes under a succession of managers and has left for a fee in the region of £1.5 million.
"This is a step into a really interesting, very strong league in which Bayerhavebeen one of the best teams for years," Fosu-Mensah told the club's official website, further confirming he will retain his No.24 shirt from United.
"I'm really looking forward to joining this team. In the past few days I've talked a lot with the coach, and conversations with Simon Rolfes and Rudi Voller have convinced me that there are great prospects in Leverkusen."
Although he featured eight times in the Premier League during his maiden season, Fosu-Mensah only managed to double that total across the rest of his career at Old Trafford.
He then spent the 2018-19 campaign on loan with Fulham, though neither stay led to a full-time deal, leaving him once again competing for limited minutes across last term.
That had led to speculation that he would seek a permanent move away from United, and his transfer brings an end to his Premier League career for the near future.
"Timothy Fosu-Mensah is a technically adept, fast and physically strong defender who can be used both as a right-back and in the centre," Leverkusen sports director Simon Rolfes added on the defender's capture.