Their contracts are not being renewed when they expire at the end of June.
The pair have amassed 350 appearances between them and have made significant contributions over the past six years.
Maghoma, 32, joined Blues under Gary Rowett on a free transfer from Sheffield Wednesday in the summer of 2015.
His clever and effective wing play, combined with a fair share of important goals and assists allied to the team framework, made him a key cog in various sides.
Maghoma won the Player of the Season and Players' Player of the Season award in 2017/18.
In what was a difficult campaign that saw Blues managed by Harry Redknapp, Lee Carsley on a caretaker basis, Steve Cotterill and Garry Monk, Maghoma produced some influential performances throughout, particular during difficult periods for the team.
Grounds, in fact, was very much in contention for these honours, too, until a knee injury at Sheffield Wednesday in the February halted his form.
This season Maghoma's last appearance came in the FA Cup replay against Coventry City at the start of February. Unfortunately he tore a thigh muscle in that game but has subsequently resumed training.
Maghoma has played 21 times for Blues this campaign, 12 occasions entering the fray as a substitute, and scored on New Year's Day against Wigan Athletic.
Overall, the DR Congo international has made 180 appearances for Blues and netted 21 goals.
Grounds came to Blues on a free transfer, from Oldham Athletic, under Lee Clark in the summer of 2014.
The 32-year-old is currently Blues longest-serving player.
He established himself as first choice left-back and was a constant on the teamsheet for just under four straight seasons, seeing off various challengers, until Monk's arrival.
Sound, measured and an intelligent reader of the game, Grounds has been one of Blues most consistent and dependable players and goes about his duty without fuss.
He spent the 2018/19 season on loan at Bolton Wanderers as Blues brought in Kristian Pedersen.
Although assimilated back into the First Team squad this campaign he has not been involved in senior action, instead a handful of Under-23s matches.
The last of Grounds' 170 appearances for Blues was at Wolves in April 2018. He has scored five times for Blues.
The Club would like to offer its sincerest thanks to both Jacques and Jonathan for their contributions over the years and we wish them every success in the future.