The couple met and fell in love on the sets of the final film in the franchise "Harry Potter And The Deathly Hallows: Part 2" in 2010 and had been dating each other for the past two years, reported Daily Mail online.
Bower, 23, who played dark wizard Gellert Grindelwald in the last Potter film, confirmed that the couple had split up, saying he was heartbroken.
His former fiancee, who starred as Ginny Weasley in the franchise, has left the London townhouse they were sharing.
"They have split but it is amicable," a source said.
Wright, 21, is filming her new film "Shakespeare's Daughter", in the US.
Bower, who played the role of Caius in "The Twilight Saga: New Moon", is moving to Toronto and then Los Angeles for five months to make "The Mortal Instruments", with Lily Collins.