Manchester United have agreed to sell Angel Di Maria to Paris St Germain for 63million euros.
The former Stuttgart full-back, who has been capped eight times by Germany, has signed a two-year deal with the Champions League participants and will link up with his new team-mates today.
"We've got an experienced, attack-minded right full-back in Roberto Hilbert," said Leverkusen's general manager Wolfgang Holzhauser.
"He has international experience and makes us tactically more flexible, particularly down the right."
Hilbert, 28, won the Bundesliga with Stuttgart in 2007 before moving to Turkey in 2010, winning the Turkish cup at the end of his first season with Besiktas.
He now returns to the Bundesliga keen to perform at the highest level once again.
"I'm delighted that this transfer has worked out," he said on his new club's website. "Bayer Leverkusen are a great club who are giving me the chance to prove myself in the Bundesliga and also in the Champions League."