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.
Liverpool did not reveal the transfer fee but Southampton announced it was “a new world record for a defender’’.
Media reports in England however have it that it was a 75 million pounds ($100.49 million) deal.
That figure would eclipse the huge fees Manchester City spent on both Tottenham Hotspur’s Kyle Walker (£50 million) and Monaco’s Benjamin Mendy (£52 million) last summer.
“The Reds have agreed a deal with the south coast club, and the player himself, which will see the 26-year-old defender move to Anfield when the transfer window reopens on Jan. 1,” Liverpool said in a statement.
“The Netherlands international will be assigned squad number four, upon his arrival at Liverpool.”
The signing will be seen as a major coup for the Reds, whose defensive problems have been highlighted during this season almost as much as their attacking prowess.
Under manager Juergen Klopp, they were pursuing Van Dijk’s signature in the summer before the Merseyside club ran into trouble and had to apologise for making an illegal approach for him.
Van Dijk, who has never hidden his admiration for Liverpool, said in a statement he was “delighted and honoured” to sign.
“Today is a proud day for me and my family as I join one of the biggest clubs in world football!” he said on Twitter.
“I can’t wait to pull on the famous red shirt for the first time in front of the Kop and will give everything I have to try and help this great club achieve something special in the years to come.”
Two other major Premier League clubs, leaders Manchester City and champions Chelsea, had also been reported to have sought Van Dijk’s signature but Liverpool won the race.
It ends a long chase for the side currently lying fourth in the Premier League.
Liverpool had originally been ready to pay about £60 million in the summer for Van Dijk when it became clear he wanted to join them.
Southampton, though, were angry that the information about a deal was leaked before any fee had been agreed.
This prompted the Saints to complain to the Premier League and Liverpool to apologise and agree not to pursue the signing.
Van Dijk then missed the season’s start, amid suggestions he was disgruntled at being denied a move.
But he was eventually brought back into the fold under new manager Mauricio Pellegrino only to be left out again in recent matches.
This time, it was presumed this was so because the deal with Liverpool was being ironed out.
Van Dijk had signed a new six-year contract with Southampton last year, having joined from Celtic for £13 million in September 2015.