Conroy spent the first half of the season at Aldershot Town, making 17 appearances for the Shots.
He returned to Chelsea earlier today, before joining Swindon on a permanent deal.
And the defender has now revealed he can't wait to get on the field for his new side.
“I'm very excited to be here," Conroy told Swindon's official website. “Swindon is a very big club and I'm just looking forward to getting started and playing.
“I found out on Wednesday that coming here was a possibility and it just all happened really quickly.
“I'm just happy to properly join and get everything signed – I'm looking forward to playing!
“Everyone knows about Swindon so it is obviously a very big club and to be involved with the first-team here is very exciting."