Van Dijk joined Premier League outfit Southampton from Scottish Premiership champions Celtic on a five-year contract.
Lawwell has revealed that the 24-year-old did not want to stay at Celtic any longer.
“We didn’t have to sell van Dijk,” the Celtic chief executive told The Scottish Sun. “We could have have kept him to his contract which had two years left.
“We would have preferred to do that. But the dynamic had changed. Virgil was desperate to go. He’s gone to Southampton for five times his salary.
“If we had held on to him for another two years we wouldn’t have had a very happy player. Now, over the next few years he’s going to be earning £45,000-a-week at Southampton.”
Van Dijk was one of the best players for Celtic for the past two years and was arguably the best centre-back in the Scottish Premiership.
It will be interesting to see how the Dutchman does in the Premier League, especially as there will be pressure on him to hit the ground running at Southampton.
The Saints will return to league action on Saturday afternoon, when they take on West Bromwich Albion away from home at The Hawthorns.