Lawrence starred in the World Cup for Trinidad & Tobago

Lawrence, 32, asked for the move after League One side Swansea made their interest known with an initial bid.

Swansea have been looking for a central defender since Garry Monk was ruled out until the New Year with a knee injury.

"At 32 this is a great move for me. It's a big club and a big challenge for me. I'm really looking forward to it," Lawrence told the Swansea website.

"Obviously I'm sorry to leave Wrexham because I've enjoyed my five years at the club. The fans were brilliant to me."

I must stress that we did our best to persuade Dennis to stay Wrexham manager Denis Smith

Lawrence, who joined Wrexham on a free transfer in 2001, had one year left on his contract at the Racecourse.

The 6ft 7in Trinidad and Tobago international is expected to make his Swansea debut in Saturday's home league match with Doncaster.

"It's a great acquisition for us. Denis proved in the World Cup just what a quality defender he is," said Swansea manager Kenny Jackett.

"I'm sure he'll make his huge presence felt in the heart of the defence."

Wrexham manager Denis Smith said he was saddened by Lawrence's decision to leave the club.

"I'm disappointed to see Dennis go, as he has been an excellent player and ambassador for Wrexham FC," said Dragons manager Denis Smith.

"Following earlier interest from Swansea, I thought we had settled the matter and he would be staying.

"But following a written transfer request from the player and an increased bid, it was decided that it would be in the best interests of all concerned if he was allowed to leave.

"I must stress that we did our best to persuade Dennis to stay, as he has been a super servant for the club."