Cole still had a year left on his contract but he has had a series of fall-outs with Graeme Souness who made it clear he was no longer his first choice following the arrival of Paul Dickov.
Fulham boss Chris Coleman expressed his delight at capturing a quality player.
"We're delighted to have signed Andy," Coleman declared. "His pedigree speaks for itself. He had a medical yesterday and everything was fine. He joins us for training on Tuesday.
"There are just one or two things that Blackburn have to sign for his release, but everything has been organised and he's a Fulham player."
"We've been looking at Andy for some time and now was the right moment to move for him, so that's what we've done. It didn't work out for him at Blackburn for various reasons but that's nothing to do with us. We're very pleased he's a Fulham player and we're looking forward to working with him. We need 11 hungry players on the pitch and Andy is still hungry. He wants to succeed and that's why we've brought him to the club."