The pair worked together at the NRL club from 2018 to 2019, which proved to be the final two seasons of Burgess' illustrious career.
Peters was an assistant coach to Anthony Seibold and Wayne Bennett at the Rabbitohs, and Burgess has good memories of the man who will replace Tony Smith in the Hull KR hot seat at the end of this year.
The Dewsbury-born Burgess, who began his career at Bradford Bulls before taking the NRL by storm with Souths, believes Peters will be a hit in Super League.
"Congrats to @hullkrofficial," tweeted the former dual-code international.
"Top bloke and will be great for the club."
Peters will take over from Smith following the conclusion of the 2022 season after signing a three-year deal earlier this week.
The 43-year-old began coaching in the NRL with Manly Sea Eagles and is now part of Adam O'Brien's backroom team at Newcastle Knights.
During his playing days, Peters enjoyed spells with Gateshead Thunder, Wigan Warriors and Widnes Vikings in Super League.
Hull KR were left looking for a new head coach after Smith decided against renewing his contract.