"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.
In fact, the report claims that a deal could even be fully agreed before the official opening of the transfer window on Monday - with talks progressing massively over the last few days.
Former Liverpool defender Jamie Carragher struck a more positive tone, noting that Van Dijk is better than he was in many departments.
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Van Dijk 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.
Van Dijk, who has never hidden his admiration for Liverpool, said in a statement he was "delighted and honoured" to sign.
Van Dijk is understood to have undergone a medical on Wednesday, and the Reds announced the move will be finalised when the transfer window opens on January 1.
Virgil van Dijk has spoken of his joy at becoming a Liverpool player, after agreeing a world record switch from Southampton.
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Liverpool confirmed Wednesday an agreement had been reached to sign Dutch worldwide Virgil van Dijk.
Liverpool are now fourth in the league table, while Southampton on 14th.
In return, Liverpool have forked out STG283 million ($A555 million) to the Saints.
Southampton were furious at the leak of information before a fee had been agreed and their complaint to the Premier League prompted an apology from Liverpool and an agreement not to pursue the deal.
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The player only signed a new six-year contract last year, having joined the Saints from Celtic for £13m in September 2015.