Forwards David Clarkson, 29, and Paul Heffernan, 33 and defender Kyle Benedictus, 23, will not be offered new contracts.
The club had already released midfield duo Iain Davidson and Jamie Reid.
Englishman Hemmings, 23, is currently with Barnsley after previous spells with Rangers and Cowdenbeath.
He will join Paul Hartley's side on 1 July on a three-year deal.
The forward has scored five goals for English League One side Barnsley this season and has 29 goals from his previous spells in Scotland.
Former Motherwell striker Clarkson joined Dundee in September and soon scored eight goals in eight successive games. However, the Scotland cap has added to his season's tally only once since November.
Irishman Heffernan, who has played for several clubs in England and Scotland, moved to Dens Park in February and his only goal so far was in April's city derby win over Dundee United.
Dundee-born Benedictus is currently on loan at Scottish Championship side Alloa Athletic and made his senior debut with the Dens Park side in 2008.
Dundee have secured striker Kane Hemmings on a pre-contract agreement as the club has confirmed more players will be leaving Dens Park.