The 26-year old has penned a two-year contract with the Championship club who he will join on July 1 once his Fir Park deal expires.
"It feels brilliant to be a Birmingham City player," Randolph told the club's official website. "I'm just happy to get it all done and I'm looking forward to getting started.
"I wanted to come here because of the size of the club. The manager wants to achieve things at this club and after speaking to him I was sold.
"I've proven myself in the SPL and now it's time that I came down here and did the same in the Championship."
The deal sees Randolph return to English football after kicking off his career with Charlton Athletic where he had subsequent loan deals with the likes of Accrington Stanley, Bury and Hereford United prior to his 2010 shift to Motherwell.