Sources told ESPN that Diaz was Jurgen Klopp's primary target for the summer transfer window, but the club brought forward their plans to sign the winger when Spurs opened talks with Porto last week. Sources added that Diaz has signed a contract until 2027 at the club.
"I could not be happier that we've been able to get this deal done and bring Luis to Liverpool," Klopp said.
"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, we saw what a danger he is, how fast he is and how his mentality was to help his team.
"We know Porto is an outstanding club who nurture players in the best possible way and provide a brilliant football education. They are a class club and, I have to say, have been tough negotiators."
Liverpool faced a host of logistical issues in signing Diaz, who is in South America with the Colombia squad for their World Cup qualifiers against Peru and Argentina, but were able to complete the deal ahead of the by the 11 p.m. GMT (5 p.m. ET) transfer deadline on Monday. Diaz requires a work permit to enter the United Kingdom and therefore will unlikely arrive in Liverpool until the end of next week at the earliest.
"We also have to say thank you to the Colombia FA for being so helpful in allowing us the time to complete this deal," Klopp added. "They have a big game on Tuesday and I know as well as anyone how important preparation is for matches, so for them to allow us a few hours to finalise the transfer without impacting their training was greatly appreciated.
"I also must make clear my appreciation to our ownership and football operations team for how they have managed to act so decisively to get this done.
"Luis is a player we believe will make us better now and in the future. He is the player we really wanted and they've made it happen, so I am very happy."
The winger has been in fine form for Porto this season, scoring 14 goals in 18 games in Portugal's Primeira Liga, as well as scoring twice in this season's Champions League group stage.
Diaz joined Porto from Colombian side Atletico Junior in 2019 and has made 125 appearances, scoring 41 goals and registering 20 assists.