Burgess, a 191 cm forward/ruck, will be in the red, gold and blue at least until the end of 2024, while Casboult has signed just the one-year deal.
After cementing his spot in the Suns' best 22 in season 2021, playing 19 of 22 games, Burgess found opportunities hard to come by in 2022, managing only two games as the new forward combination of Mabior Chol and Casboult was a success.
Despite being on the outer, Burgess took every chance in the VFL, booting 63 goals to win the competition's goalkicking award.
His phenomenal performances included a seven-goal haul against Collingwood and two six-goal outings against Sandringham and GWS, and warranted interest from the Crows and Saints, according to AFL.com.au.
With the Suns having a bevy of tall forwards, plus the return of Ben King from an ACL, Burgess will be in a fight to put himself to solidify his spot as one of the Suns' main forwards.
Casboult enjoyed a career-best campaign in 2022, booting 35 goals from 21 games.
“Both Chris and Levi have been important to the success of our club and are key re-signings as we aim to maintain our depth of tall forwards,” Suns list manager Craig Cameron said in a club statement.
“Chris was impressive at VFL level and earned a call-up to the AFL team on multiple occasions. He loves the club and we're pleased to be able to extend him.
“Levi has been a valued acquisition for our club and played an extremely important role for us this season, so we are excited to see his career continue with the SUNS.”
The Suns still have some wheeling and dealing to do in the trade period, with Izak Rankine requesting a trade to Adelaide, Jack Bowes nominating Geelong as his club of choice, forward Josh Corbett nominating Fremantle, and WA product Jeremy Sharp also on the radar of both Fremantle and West Coast.