The English national joined the Rabbitohs' coaching staff as an assistant in 2020, the season after a shoulder injury ended his 182-game NRL career.
As a player, Burgess first made a name for himself with Super League outfit Bradford in the late 2000s.
The forward went on to become synonymous with South Sydney, receiving the Clive Churchill Medal as player of the match in their drought-breaking 2014 grand final victory.
He has since served as an assistant to current Souths boss Jason Demetriou and his predecessor Wayne Bennett.
As a head coach, Burgess led the Russell Crowe-backed Orara Valley Axemen to the grand final in last year's Group 2 rugby league competition.
The Rabbitohs said Burgess left the club with their blessing.
"We still have an opportunity to play some great football for the remainder of the year, and to do so alongside our current staff and squad is my focus," Burgess said.
Burgess has signed a two-year contract with Warrington, who sacked head coach Darryl Powell last month following a 42-6 loss to last-placed Wakefield Trinity.
Matt Dufty, Paul Vaughan and Sam Kasiano are among the ex-NRL players currently on the Wolves' roster.
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