The 25-year-old Diaz signed a contract till 2027 for a reported fee of £37.5 million ($50 million), with a further £12.5 million in potential bonuses.
There is no resolution in sight to protracted talks over a contract extension for Salah, who is presently away at the Africa Cup of Nations.
“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 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.
Diaz would add fresh blood to the Liverpool forward line and comes with a burgeoning reputation after scoring 16 goals in 28 games for Porto this season.
He was also top scorer alongside Lionel Messi at last year’s Copa America with four goals.