Brough had his contract with United cancelled by mutual consent towards the end of last season and has since been playing for Unibond League side Barrow.
He had a trial with Boston pre-season, aand is one of two new signings made by the Pilgrims today to cover an injury crisis.
Brough, who made 57 first team appearances for Scunthorpe and scored three goals, is joined by Adebayo Akinfenwa from League of Wales outfit Barry Town.