His representatives said he had died "suddenly" following a short illness.
Writing on his Facebook page, his daughter Lauren said she was "utterly heartbroken" that her "darling father" had died.
She said he had been "sick for a while" but there had been a "rapid decline over the past week".
Cross, who died in Vienna, Austria, had two children, Lauren and Theo.
His representatives said he had just finishing shooting horror film The Devil's Light and later this year will appear in a leading role in the romantic drama film Last Letter From Your Lover.
