The 18-year-old has featured regularly in the Leeds reserves this season and made his first senior outing in Tuesday night's 3-1 defeat to Southend in the Third Round of the Carling Cup.
Bayly joined United after playing for Cherry Orchard and Shelbourne in his native Ireland and has been a regular member of the country's highly-successful youth squads over the past few seasons.
"It is terrific news, I am absolutely thrilled," Bayly told www.stellargroup.co.uk
"I am really enjoying my football here. It is a huge club and although the first team are struggling a bit at the moment I am sure that things will turn around soon.
"We have brought in a new manager who will no doubt have some new ideas and I am very much looking forward to working for two such great former players as Dennis Wise and Gus Poyet.
"It was great to make my debut the other night. Although the result went against us, it was the next step up on the ladder for me and now I've had a taste I am eager to try and force my way into the team on a more regular basis."