The fee for Van Dijk, who joined Southampton from Celtic in 2015 for £13million, will be a world record for a defender.
The fee would be the most ever paid for a defender - Manchester City set a record when they paid £52m Monaco's Benjamin Mendy in July.
The Reds were left celebrating on Wednesday as they announced that Southampton's star would be finally joining the club after a protracted transfer saga.
But the move fell through when Liverpool were forced to make a public apology after being accused of making an illegal approach for the player.
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"Delighted and honoured to have agreed to become a Liverpool FC player", Van Dijk wrote.
The 26-year-old will wear squad number 4 on arrival at Anfield.
Van Dijk was absent as Southampton were battered 5-2 by Tottenham at Wembley on Boxing Day and he has not played since Saints' December 13 defeat to Leicester City.
After a summer transfer window saga of vast annoyance and frustration for fans, management and Southampton's Virgil van Dijk himself, there finally seems to be some light at the end of the tunnel.
Southampton confirmed the world-record deal and sent their best wishes to Van Dijk, who admitted he owed a debt to the south coast club.
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Many Saints fans will be disappointed to let yet another top player slip through their fingers to Liverpool - following the departures of Sadio Mane, Dejan Lovren, Nathaniel Clyne, Adam Lallana and the now-retired Rickie Lambert.
"Despite a hard last few months, I have thoroughly enjoyed my time at Saints and have made friends for life at the club".
"Liverpool need defenders and have to pay to get him".
A statement from Liverpool read: "Liverpool Football Club can confirm they have reached an agreement with Southampton for the transfer of Virgil van Dijk".
Van Dijk's first game is likely to be the FA Cup third round Merseyside derby with Everton.
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