The 19-year-old will join Hearts' Adam King in the Welsh outfit's under-21 squad.
But Fulton, son of former Hearts and Falkirk midfielder Stevie, said: "The style here really suits me. I like to be on the ball and pass it about.
"I know I will be stepping straight into the under-21s set up, but I see it as an avenue to the first team. I see this as a big opportunity for me."