News emerged on Wednesday evening of a move being imminent, and both Liverpool and Southampton confirmed the news on their official websites at 6pm.
Netherlands international Van Dijk is expected to cost the Reds around £75m, making him the most expensive defender of all time.
A statement on Liverpool's official website read: "Liverpool Football Club can confirm they have reached an agreement with Southampton for the transfer of Virgil van Dijk.
"The Reds have agreed a deal with the South Coast club, and the player himself, that will see the 26-year-old defender move to Anfield when the transfer window re-opens on January 1, 2018."
Van Dijk, who has been left out of the Saints' squad in recent games, will wear the number four shirt at Anfield.