The full-back, capped once by England, joins Leeds for £10 million ($13.5m) and will aim to help the Whites stay in the Premier League this season.
“Obviously to join a club of this size and to have the history it has had, and being back in the Premier League was a massive thing for me, so I'm over the moon to have joined,” Justin told club website.
“It's been a while since I've known of the interest, but obviously I was still a Leicester player, so I had to give my all for Leicester whilst I was there.
“That's something obviously that you can expect from me when I put on a Leeds shirt, is to give my all when I'm on the pitch. But for it to finally have happened, it’s taken a weight off my shoulders for sure.
“Everyone that I've spoken to about the club and the area has had great things to say about it. So I'm excited to join the lads and get to work."
Justin could make his Leeds debut when they face Championship side Sheffield Wednesday in the second round of the Carabao Cup on Tuesday night.