The 19-year-old was named the player-of-the-year at the Blue Square South side last season and was reportedly interesting Fulham, Nottingham Forest and Brentford.
The former Charlton Athletic youngster has agreed a two-year contract with the Glovers.
"There's been a lot of interest in Kieran and he has been on our radar for about six months now," the Glovers' assistant manager Steve Thompson said.
"We have had him watched and Fulham were interested in him, but we have jumped in and he is set to sign a two-year contract."