The 21-year-old impressed manager Jackie McNamara during a trial last week and played an hour of Saturday’s pre-season friendly against Bolton Wanderers.
Simpson began his youth career with Oldham Athletic before signing professional terms with the League One outfit in 2013, despite reported interest from Manchester United and Celtic.
During his first senior season with the Latics, the 6`3” shot-stopper enjoyed loan spells with both Evo-Stik Northern Premier League Premier Division outfit Workington AFC and current Premier League champions Leicester City.
After failing to make a senior appearance at Boundary Park, however, Simpson switched permanently to Accrington Stanley in August 2014, where he featured nine times before departing the Wham Stadium at the turn of the year.
Following a trial at Premier League outfit Watford last season, the ‘keeper signed an eight-month deal with the Hornets before departing at the end of his contract earlier this summer.