United and Chesterfield agreed a fee for the central defender on Tuesday but the formalities of the deal were completed on Wednesday evening.
Last month United had two bids for the defender rejected by Chesterfield but a revived bid on Tuesday was accepted.
The Yorkshire born defender came through the Academy ranks at Hull City and he made his first team debut for the Tigers in 2008.
During his time at Hull City the defender spent loan spells at Carlisle United, Huddersfield Town and Chesterfield.
After a successful loan spell the 22-year-old signed on a permanent basis at Chesterfield and made over 50 appearances last season.
Last season Liam helped Chesterfield win the League Two title and was named in the PFA Team of the Year.
United and Chesterfield met each other in a pre-season friendly this summer where Liam was a solid presence on the field during the 2-2 draw.
United head coach David Hockaday said: “Liam has lots of potential as a defender. He has a great left foot and bringing him to the club is great business.”
Spireites boss Paul Cook said: "It has been a pleasure to work with Liam, who was a key member of our title-winning squad last season. I would like to thank him for his valuable contribution and wish him all the best for the future."