Fernando Morientes has completed his £6.3m move to Liverpool after earlier passing a medical examination.
"Fernando Morientes is now officially a Liverpool player," club spokesman Ian Cotton confirmed.
The Spanish international has signed a three-and-a-half year contract and will be unveiled on Friday at 1300 GMT.
Morientes, 28, told the Liverpool website: "I am excited about playing for Liverpool and it's the biggest decision of my football life."
Manager Rafa Benitez revealed his excitement at the prospect of partnering Morientes with Milan Baros and hinted it could happen in Saturday's match against Manchester United.
Benitez said: "Morientes is important to us. He is good in the air, he is a good finisher and can shoot with both feet.
"We need a target man with experience - for the supporters, for the team and for the players.
"He is not the quickest but he can play with Baros and they could form a good partnership because one is good in the air and the other is quick.
"He also has the mentality to go straight into a game like Saturday's if necessary."
Liverpool will pay £5.5m initially but the fee will rise to the full asking price depending on certain clauses.
Those clauses are believed to be linked to the striker making a certain number of appearances for Liverpool.
Morientes added: "I want to play and I had several offers, but I think the best for me and my family was Liverpool's.
"I am happy for that reason, but sad because it has been eight years here at Madrid and I will never forget them. This is a new stage in my life and I am excited about it."
Real Madrid coach Wanderley Luxemburgo earlier said he was sorry to see Morientes leave.
"I like Morientes because of his playing style. But Real Madrid were already talking about [his transfer] and I couldn't do anything. I spoke to him but [the move] was what the player wanted."
Real Madrid general manager Emilio Butragueno said, "It hasn't been easy for us to allow him to leave."
Morientes, highly prized in French football after his goals while on loan steered Monaco to the final of the Champions League last season, could have chosen to join Lyon.
Lyon made a late bid of £6m - considerably more than Liverpool's initial £3.5m offer - which was rejected.
Morientes was the top scorer for Monaco last season on their Champions League run, and was recalled to Real when new manager Jose Camacho took over in July 2004.
But Camacho lasted only until September, when he was replaced by Mariano Garcia Remon, who in turn was ousted in favour of Luxemburgo in December.
Throughout the changes, however, Morientes has remained fourth-choice at the Bernabeu behind Ronaldo, Raul and Michael Owen, who left Liverpool for Spain in the summer.
Morientes, who has previously outlined his admiration for Benitez, becomes the fifth Spaniard to be signed for Liverpool by their compatriot manager, after Luis Garcia, Xabi Alonso, Josemi and Antonio Nunez.
Argentine defender Mauricio Pellegrino has also joined from Benitez's old club Valencia.
He marked his debut with a goal in the 3-0 reserve-team victory over Chester.
Baros and Igor Biscan also featured in the game.