He has a signed a 12-month rolling contract and will continue to assistant Manager Harry Redknapp.
Groves was brought in by Redknapp after he joined the Club as interim boss in April.
Along with Steve Cotterill, he was joint First Team Coach/Assistant.
The trio helped Blues to two successive wins to end the season and thus avoid relegation from the Championship.
Groves made more than 700 appearances in a 19-year playing career that saw spells at Blackpool, Grimsby Town (twice) and West Bromwich Albion, amongst others.
The midfielder moved into management as player/boss at Grimsby in 2001.
He coached at Portsmouth and West Ham United before becoming Bournemouth youth team coach for two stints either side of the Cherries manager’s job.
He was coach at Crawley Town in 2014-15 before joining Bristol City as Academy Manager.
In March 2017 he worked at Mickleover Sports as assistant manager before Redknapp brought him to Blues for the final three games of the campaign.