Former Rovers midfielder Wellens has taken over as the new manager of the League One club, where he will again work with Hunt, who had an injury-hit spell at Leeds United from 2013 to 2015.
Hunt's former Reading manager Brian McDermott took the Republic of Ireland manager to Elland Road but his contract was cancelled after being limited to 22 appearances without scoring.
Hunt joined Swindon as player-assistant manager in November 2018, taking caretaker charge for a month when Wellens left for Salford City in November 2020.
Swindon were League Two champions in the closest thing the pair had to a full season together, handed the title on a points-per-game basis when the campaign was abandoned because of Covid-19.
Wells, who made almost 200 appearances in two spells for Doncaster, started his managerial career at Oldham Athletic.
Support The Yorkshire Post and become a subscriber today. Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you'll see fewer ads on site, get free access to our app and receive exclusive members-only offers. Click HERE to subscribe.