The Irishman has been appointed assistant manager to newly-appointed boss Richie Wellens at the Keepmoat Stadium.
Hunt reunites with Wellens after the pair guided Swindon Town to the League Two title in the 2019-20 season.
Wellens left for Salford in November but was not reunited with Hunt after he departed the County Ground a month later.
Hunt had been linked with Ipswich to become Paul Cook's right-hand man after he took charge at Portman Road in March.
However, the former striker – who scored once in 24 games when Pompey clinched the fourth-tier crown in 2017 – has instead opted for Donny.
Rovers will be vying for League One promotion with Pompey in the 2021-22 season.
Both sides spent much of this term in the play-offs before tailing off and missing out on top-six finishes.