A source close to Liverpool said the fee for the deal was £75 million, which would make van Dijk the most expensive transfer in club history and also constitute a record fee for a defender.
"Southampton have agreed a fee that will set a new world-record for a defender".
The BT Sport pundit responded to a fans tweet from 2015 after he laughed at the former Hoops striker for claiming Van Dijk was worth £20million.
Van Dijk will join up with his new side when the January transfer window opens. 'I've not seen a lot of Southampton recently but I'm not sure he's playing that well.
An official announcement from both clubs has been made with the deal to be concluded on January 1.More news: Lewandowski accused of inappropriately touching singer at holiday party
"I will always be indebted to the club for giving me the opportunity to play in the Premier League".
"I will always be indebted to the club for giving me the opportunity to play in the Premier League and despite a hard last few months I have thoroughly enjoyed my time at Saints and have made friends for life at the club. Thank you for everything".
'It's a lot of money isn't it, ' he told Sky Sports.
"Liverpool need defenders and have to pay to get him".
The signing of the in-demand centre-back was announced after the two clubs, who had failed to agree terms for the transfer during acrimonious dealings in the summer, finally reached an agreement.
Van Dijk's first game is likely to be the FA Cup third round Merseyside derby with Everton.