Thompson, 38, hails from Kendal and played more than 700 games for Morecambe, Scunthorpe, Bradford, Notts County and Wycombe.
Two years ago, he scored for Wycombe in the FA Cup against Premier League side Tottenham Hotspur at White Hart Lane.
He was due to start Saturday’s game at home to Mickleover Sports, before it was postponed 45 minutes before kick-off due to a waterlogged pitch.
Workington have also signed Scottish striker Dean Brotherston.
His previous clubs include Queen of the South and Forfar Athletic.