A left-footed central midfield player, Thomason took over as captain at the League One club last season, when he scored five goals in 46 games.
He helped Bolton secure promotion from League Two in 2020-21 and to Wembley victory in the Football League Trophy two years later.
Barrow-in-Furness-born Thomason played against Wrexham three times last season.
“We’re delighted to welcome George to the club,” said Wrexham boss Phil Parkinson.
“We’re looking forward to getting him in training with the lads later this week and fully integrating him into the group.”
