Taylor, 20, had initially joined on a short-term loan deal as cover for the injured Steve Phillips.
Boss Dario Gradio told BBC Radio Stoke: "Chelsea have been tracking him and they're pleased with him and pleased with us and he's happy here.
"He's done well, he's very quick and he keeps the ball out of the net."
The initial deal would have expired on Wednesday but Taylor was happy to stay for the remainder of the campaign.
"My plan was just to get through it and play and do as well as I could and I think the manager now knows that I can do alright in this league," he said.
"I've played more games in this month than all of last season and maybe two seasons so it's good for me to be playing."