The `Voice` coach and the Russian-born model have decided to part ways after two years of dating but Anne, 26, claims the couple still "love and respect" each other.
She said in a statement to People magazine: "Adam and I have decided to separate in an amicable and supportive manner. We still love and respect each other as friends. I wish him all the best."
A friend of the Maroon 5 frontman added to US Weekly: "He will always love and cherish her."
Adam, 33, and Anne first met at the Sports Illustrated swimsuit issue release party in Las Vegas in early 2010, where Maroon 5 performed but didn`t immediately hit it off.
Anne previously said: "He thought I was a stuck-up bitch and I kind of thought he was a d*****bag musician."
Although the couple were rumoured to have had a giant bust up earlier this year, speaking in February, Adam said he was determined to make the relationship work.
He explained: "This is the most functional relationship I`ve ever been in. I don`t want to screw it up."
Adam previously dated celebrities including Jessica Simpson, Maria Sharapova and Cameron Diaz. He had a four-year relationship with former Vogue editor Jane Herman after meeting in high school and detailed his heartbreak over their split in Maroon 5`s 2002 debut album `Songs About Jane`.