Clyne has brought an end to his three-year association with Southampton, having signed from the club from Championship side Crystal Palace back in the summer of 2012.
Signed under the management of Nigel Adkins, the defender went on to make 104 appearances for the St. Mary's side, scoring five goals in the process.
The reported fee for the 24-year-old Stockwell-born right-back is said to be in the region of £12.5m.
This represents a considerable return on Southampton's acquisition of Clyne for a fee in the region of £3m, as set by a tribunal.
Clyne was entering the final 12 months of his contract at Saints, and so the decision was taken to sell the player when he showed his reluctance to pen a new deal.
Southampton boss Ronald Koeman had set several deadlines for the England international to provide a final answer on his future, with Director of Football Les Reed explaining the reasons behind Clyne's exit.
"With Nathaniel's contract entering its final year, it was important that his future was resolved this summer," Reed said.
"With Cédric Soares now in place and it becoming clear that Nathaniel did not wish to extend his deal, we were keen to swiftly move on early in our pre-season schedule.
"We have now been able to conclude our negotiations with Liverpool, and we thank Nathaniel for his efforts during the past three seasons."
Clyne is so far the only sale from Southampton this transfer window, with Morgan Schneiderlin and Gastón Ramírez expected to follow suit in the coming weeks.