Thirty-three-year-old Constable has joined the side with a view to gaining more game time.
He joined Eastleigh in May 2014 from Oxford United shortly after the Spitfires had won promotion to the National League.
Constable joined Oxford permanently from Shrewsbury Town in July 2009 after a successful loan spell.
He was the club's top scorer for each of his six seasons at Oxford and made 204 appearances, with 67 goals.
His earlier football was spent with Cirencester Town, Chippenham Town, Walsall and Kidderminster Harriers.
Constable has featured twenty-five times so far this season for the Spitfires and will join the Dolphins ahead of tomorrow’s fixture at Braintree Town.