Tudur-Jones impressed while on trial from Welsh Premier side Bangor City, and had joined for a month.
But he caught the eye of Swindon and Tranmere, and Swans boss Kenny Jackett has moved to keep him at the club.
He told the Swansea Evening Post: "We'd settled on a month with Owain to begin with, but then Swindon and Tranmere made enquiries.
"That made the situation a little different, and it was after Owain's display in the game at Forest Green Rovers on Tuesday that I was convinced I wanted to sign him up for the year.
"Every week Owain has been with us he has improved and, at 20, I think he will keep on getting better now he's training full time."