The 18-year-old departed Elland Road in the summer and had been on trial with the Hornets.
"I'm delighted, I've had to be really patient over the summer to get this done but I'm just buzzing that it's happened now," he said.
"I was out of contract and looking for a club, and I got the opportunity to come down to Watford.
"I'm willing to take any opportunity that comes in football because I love it, and I'm delighted the decision's paid off.
"I've settled in quite well, I'm enjoying it. It's quite far from home but all of the lads have made me feel welcome."
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