Southampton centre-back Virgil van Dijk will join Liverpool when the transfer window re-opens on 1 January in a world record £75m deal.
The Netherlands international had been expected to join the Reds last summer after he handed in a transfer request.
But a move fell through when Liverpool apologised for making an alleged illegal approach for the 26-year-old.
Van Dijk said in a statement he was “delighted and honoured” to sign for the Merseyside club.
He was left out of Southampton’s squad for their 5-2 defeat by Tottenham on Tuesday, prompting speculation he was set to leave the club.
The player only signed a new six-year contract last year, having joined the Saints from Celtic for £13m in September 2015.
However, Liverpool’s interest in the summer prompted a transfer request from the player which saw him forced to train alone by manager Mauricio Pellegrino.
He returned to first team action in September, featuring in a win at Crystal Palace.
Van Dijk’s former club Celtic will benefit from the record transfer fee – the Scottish champions are understood to have had a 10% sell-on agreement on any future transfer.
Though he will join the club on 1 January, Van Dijk will not be able to register as a player until 2 January so will not be available for Liverpool’s trip to Burnley.
BBC Sport’s Simon Stone
It has cost Liverpool an additional £15m and half a season, but manager Jurgen Klopp has finally got his man.
Southampton pulled the plug on a proposed £60m deal during the summer, such was their unhappiness at the way they were being railroaded into a transfer.
However, the tell-tale sign Klopp knew who he wanted to address defensive deficiencies and wouldn’t be changing his mind came through the fact Liverpool did not try for an alternative.
After conceding 23 goals in 20 Premier League games so far, Klopp has been reminded often enough he needed to strengthen his defence.
Now he has done it, he will hope his side can retain their attacking brilliance and close the gap to Manchester United and Chelsea and, in time, start to challenge at the very top of the Premier League table.
Liverpool’s desire to sign Van Dijk comes through the size of the fee, which Manchester City – who were also interested – were not prepared to match.
As for Southampton, they have got rid of a player who clearly had no wish to remain on the south coast and generated the funds that will allow them to reinforce a squad that has struggled for the past 12 months and led to speculation manager Mauricio Pellegrino is on dodgy ground.