The 26-year-old has spent the last three seasons at Motherwell and will formally join Blues on 1 July after his current contract with the SPL outfit expires.
The Republic of Ireland international was a firm favourite at Fir Park Stadium having chalked up the club's clean sheet record, previously held by John Ruddy, on the way to helping Well reach the 2011 Scottish Cup final.
Randolph began his senior career at Charlton Athletic where he went on to enjoy loan spells with Welling United, Accrington Stanley, Gillingham, Bury and Hereford before heading north of the border on a permanent basis in July 2010.
The Bray-born gloveman is now looking forward to the next chapter of his career at St. Andrew's.
A delighted Randolph told bcfc.com: "It feels brilliant to be a Birmingham City player. 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 and it would be great to be a part of a club like this. 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."
BluesTV will bring you the first, exclusive interview with the new Blues goalkeeper shortly.