The 21-year-old attacking midfielder becomes the latest young player to make the move to the Championship.
Graham Potter said, “Taylor has been with the first-team squad for the first part of the season, he has benefitted from that time and he has made great progress during that time. He has played in the Carabao Cup ties and also made his Premier League debut, but we feel it is now important for him to play regular football during the second half of the season and he will get that opportunity with Birmingham, a club I know well.”
He scored 11 goals and contributed five assists in 48 appearances during a highly successful spell at Rovers in League One.