The Newcastle-upon-Tyne-based midfielder left Ewood Park at the end of January and has been snapped up by new boss Jamie Fullarton.
Thomson (pictured), 22 has previously played for Carlisle United and had a loan spell with Barrow AFC last season.
Fullarton has also signed 24-year-old left-back Raheem Hanley from League One side Northampton Town on loan until the end of the season.
Hanley can play left-back, central midfield and left wing started his career at home-town club Blackburn Rovers, coming through the youth ranks at Ewood Park.
He had a year with Swansea City before joining the Cobblers in June 2016.
Both came off the bench in Saturday`s away win at Woking.