The paper said the split comes just four months after rumors swirled that the pair's marriage was in trouble.
In June, Spencer, 43, was photographed at a casino in Sydney with Damian Whitewood, a professional ballroom dancer, according to the Morning Herald. Whitewood partnered with Spencer during Season 12 of Australia's "Dancing With the Stars."
The photo, which appeared in Australian media, showed the two with their arms around each other. Days after the photo surfaced, however, a photo of Crowe, 48, kissing Spencer at the Los Angeles International Airport seemed to quiet the rumors.
Crowe's rep did not respond to People magazine's request for comment.
The Morning Herald said the split is amicable and that Spencer will stay in Australia with the couple's two sons, Charles, 8, and Tennyson, 6, while Crowe focuses on his film work.
The actor is on Long Island filming the biblical epic "Noah," which also stars Emma Watson.
Crowe and Spencer first met more than 20 years ago on the set of 1990s "The Crossing" and were married in April 2003.