The Dutch defender has agreed a five-year contract and joins from Scottish side Celtic ahead of the transfer window closing later today.
Van Dijk spent just over two years in Glasgow, playing more than 100 times and scoring 15 goals.
The 24 year-old started his professional career with Groningen, where he played alongside Dušan Tadić, and has represented his country at under-21 and under-19 levels.
Executive Director of Football Les Reed said of the deal: “We’re delighted to have finally got Virgil into the club after long and lengthy negotiations.
“We’ve had Virgil in our system for a long time and have explored the possibility of signing him in previous transfer windows, and this year we had a really strong opportunity to do it.
“The Champions League had an effect on the moment of release, which we were aware of, so it was about keeping our focus and doing our due diligence before eventually getting him over the line.
“He’s still a young man but a very mature young man who has played a very good level of football at Celtic and in Europe. He’s had an excellent upbringing and still has a lot of time ahead of him.
“Virgil has signed a long-term contract, so clearly sees a strong future here with us. He’s young, hungry and wants to prove himself.”
Van Dijk added: “I’m delighted. It was a very easy decision to join this club.
“This is a very ambitious club, who have been doing very well in the last couple of years. It’s a great place to be and it’s the right step for me.
“For me now to get the opportunity to play in the Premier League is unbelievable and I will enjoy it.
“I know it’s an ambitious club – they have been through a lot throughout the years. They are trying to play football and that’s something that really attracted me.
“I’m so excited. I hope to settle in really quick, get everything around football sorted, start playing and enjoying it because the most important thing in football is to have fun and enjoy every day.”