The Reds have been chasing the 22-year-old for much of the summer, with Brendan Rodgers having made acquiring a left-back one of his transfer priorities.
Anfield bosses withdrew from negotiations last month but have returned with an improved bid for Moreno, rumoured to be in the region of £12m, after missing out on Ben Davies to Tottenham Hotspur.
The Spain international, who was omitted from Sevilla's Super League defeat to Real Madrid on Tuesday, will now undergo a medical and discuss personal terms ahead of finalising his switch to Merseyside.
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."
Moreno, who is poised to become Liverpool's eight signing of the current window, was seen tearfully hugging his Sevilla teammates upon the conclusion of their all-La Liga clash in Cardiff.