Godleman, 33, had led Derbyshire since taking over from Wayne Madsen ahead of the 2016 season, although he was not involved in the Blast side last season, Shan Masood taking over the captaincy with du Plooy as his deputy.
Godleman endured a tough summer with the bat in the Championship, failing to pass 50 until the final innings of the campaign - his 158 against Leicestershire represented more than a third of his season's runs - and agreed to the change after chatting to Derbyshire's coach, Mickey Arthur.
"I sat down with Mickey and we had a good catch-up about the season and my thoughts about captaincy, future leadership and my seven seasons as captain," he said.
"I have thoroughly enjoyed my time as captain but reflecting on this season I think that with Mickey coming in and giving the club new impetus, the time is now right for me to hand over the reins to a new leadership group as Wayne Madsen did to me in 2016.
"Seven seasons as a captain is a long time and the highlights for me will always be the strong personal relationships I've built with players past and present both on and off the field, while I am particularly proud to have led the club to their first T20 Finals Day in 2019.
"I very much hope that I can continue to be successful with Derbyshire, scoring lots of runs in all formats, and look forward to providing any support and insight I can to Leus."
Du Plooy, 27, joined Derbyshire in 2019 and is a regular in the side across formats, although involvement in the Hundred might limit his availability for the one-day cup. He was born in South Africa but qualifies as a local through a Hungarian passport.
Arthur said: "Billy has led the team with great purpose and will continue to be a senior figure within our squad, but we both feel the time is right to make this change and restructure the leadership team ahead of the 2023 season.
"For more than half-a-decade, Billy has been a dedicated Derbyshire captain, however now we have the opportunity for a new voice, in Leus, to lead the team and bring a fresh approach.
"Billy can now focus on what he does best, scoring runs for Derbyshire, without having the pressure of captaincy. His record is one that most sides would love to have in their ranks, and I hope we can see more of his quality next season."