"Liverpool Football Club have completed the signing of Luis Diaz from FC Porto, subject to the successful granting of a work permit and international clearance," Liverpool said in a statement on their website.
"He joins Liverpool after two-and-a-half seasons with FC Porto, where he made 125 appearances and scored 41 goals."
Diaz was rumoured to be Liverpool manager Jurgen Klopp's primary target for the summer transfer window, but growing interest in the player, most notably from Tottenham Hotspur, forced the Reds to move early.
He is presently on international duty with Colombia for 2022 World Cup qualifying matches.
Liverpool manager Jurgen Klopp expressed his delight at the signing of Diaz.
"I could not be happier that we've been able to get this deal done and bring Luis to Liverpool", said Klopp.
"I have always been a believer in only signing players in January if you would want to sign them in the summer, and that's very much the case with Luis.
"He is an outstanding player and someone we've been tracking for a very long time. This team deserved to add quality and when we played against Luis earlier this season (they were in the same Champions League group), we saw what a danger he is, how fast he is and how his mentality was to help his team."
Liverpool sent a delegation to Argentina -- where Colombia play on Tuesday -- to conduct a medical so the move could be completed before the January transfer window closed.
Salah and Liverpool team-mates Sadio Mane and Roberto Firmino will all be out of contract in the summer of 2023, by which point they would all be aged 31.