Bellamy only joined Rovers from Newcastle United less than 12 months ago but after signing for Liverpool, the Welsh international admitted that he couldn't snub a move to the Merseyside club.
"The fact that it was Liverpool made it impossible for me to turn down the move, as I’m a fan it doesn't matter what club I was at, my move to Liverpool is a dream come true," Bellamy said.
Liverpool who recently sold Spanish striker Fernando Morientes to Valencia and are ready to listen to offers for Djibril Cisse are believed to have paid around six million pounds for the former Norwich City prodigy.
Bellamy praised his former employers for helping him rejuvenate his career after the bust up he had with former coach at Newcastle Graeme Souness.
"I had a lot of friends at Blackburn, the players, the coaching staff, the chairman are all great people and I owe them a lot, a hell of a lot to be honest," the 26-year-old striker said.
"They helped me to improve and they were there at an awkward time of me, but I've talked to a lot of players and they know the situation."