The Oscar winner and singer Spencer wed in 2003 and have two sons, Charles, eight, and Tennyson, six.
The Sydney Morning Herald reports the split is amicable.
The couple first met 22 years ago on the set of the movie The Crossing.
Crowe, 48, is currently filming Noah in the U.S. while Spencer is at home in Sydney with the couple’s boys.
As rumours of the split surfaced late on Saturday (13Oct12), Crowe was co-hosting The Indoor Garden Party with pal Alan Doyle at the Gramercy Theatre in New York.
The Gladiator star, who is a frequent Twitter user, has yet to comment on the break-up stories – his last posts focused on Saturday night’s music and comedy concert and his cycling and work-out regimen.
Hours before news of the split leaked, he wrote, “yesterday 11.6km bike ride to work, 30 mins (minutes) yoga, light weights today so far 14.5 km stat bike, 20 mins light weights.”