Shroot has only been at Birmingham since January after playing non league at Staines Town, AFC Wimbledon and Harrow Borough
Brewers Boss Paul Peschisolido is Excited by the clubs latest signing and said: "Hopefully, Robin will come to us as a young and hungry player with a point to prove.
"Birmingham regard him as a player with a lot of potential, but right now they’re building a squad for the Premier League."
"He’s a very clever and tricky footballer who can score goals," said the Brewers boss.