Credit: Jon Kopaloff/FilmMagic

Aussie actress Abbie Cornish and Ryan Phillippe have split, her rep confirms to

On Sunday, Cornish, 27, was spotted moving out of the Los Angeles home she shared with Phillippe, 35.

"He called her to end the relationship," a source tells Us. "They had grown apart. She flew into town yesterday to move out, as he asked her to so."

Cornish and Phillippe, who met on the set of the war drama Stop-Loss, began dating in 2006 - around the same time he and Reese Witherspoon announced they were separating after seven years of marriage. (Phillippe has two children with Witherspoon, daughter Ava, 10, and son Deacon, 6.)

Last fall, Cornish told W magazine that being linked to the collapse of Phillippe's marriage was "a really difficult time for me. In a normal, successful career, someone usually learns these things bit by bit. For me, it was like night and day. I woke up one day and there was this whole new thing I had to process and deal with."

Asked if she'll wed Phillippe one day, she said, "I don't know [if we have plans in that direction]."