Brendan Rodgers made signing a left-back his priority earlier this summer and singled out the 22-year-old as his number one target.
Sevilla insisted that Moreno was going nowhere unless their 20 million euro asking price was met with manager Unai Emery insisting on Monday that he would play in the UEFA Super Cup against Real Madrid.
However, Liverpool chief executive Ian Ayre managed to thrash out a deal for Moreno in Cardiff before the game that Real won 2-0, and the player was withdrawn from the side.
The Spain international, who came through his home-town club’s youth system, is now set to undergo a medical at Anfield and discuss personal terms.
A statement on the Liverpool club website read: "Liverpool can confirm they have reached an agreement with Sevilla for the transfer of Spain international full-back Alberto Moreno.
"The Reds will proceed with the formalities of finalising the deal for the 22-year-old over the coming days and will make no further announcement until it is complete."
There were emotional scenes on Tuesday night in Cardiff after the Super Cup among the Sevilla players and staff who were hugging a tearful Moreno on the pitch.
Sevilla coach Emery insisted Moreno would leave with the club's blessing and said: "We didn't have any clear expectation (about the transfer being completed), but it was in our minds.
"This has been in the offing for a month and a half or two. We were aware of the need to take him out of the squad. And we were in England and close to the teams who are interested in Alberto. Maybe decisions are speeding up because we are getting towards the end of the transfer window (on August 31).
"We want to wish all the best to Alberto Moreno and we need to continue with our path. He's a player we can no longer count on."
Liverpool open their Premier League campaign at home to Southampton - live on Sky Sports 1HD - on Sunday at 1.30pm.
@o.k, you do realise we were heavily linked with Shaw before yous signed him? Besides it is perfectly reasonable to compare two signings of the same position. You vastly overpaid for Shaw, we got a bargain for Moreno, hoping it happens without a glitch. United and Liverpool are rivals and that's the cities as much as the football clubs, so there will always be one-upmanship. United fans are concerned/fascinated/obsessed by all things Liverpool so your statement is a bit silly.- lfcfan80