The split was announced at a celebration of Minogue's career, the Sunday Mirror reported Saturday.
Minogue, 44, has said that she wants to focus on her acting career, a source close to the star said.
"Kylie's decision to stop recording for the time being and part company with Terry has come as a massive shock," the source said. "Ever since she broke into the charts in the 80s Terry has been the man behind the scenes. But now Kylie is saying she wants to pull back from the pressures that come with a music career. She says she's determined to devote more time both to herself and to her career as an actress."
Meanwhile, there seems to be no bad feelings between the two, as Minogue thanked Blamey in a speech last week, The Hollywood Reporter said.
She thanked him "for helping a 19-year-old girl take on the world and become a woman and an artist." She later toasted, "Here's to the future."