The 22-year-old has just returned to Hull following an impressive loan stint with Charlton Athletic - and they pushed hard to re-sign him at The Valley.
Sky Sports understands that the likes of Leicester and Ipswich were also keen, but Brian McDermott has beaten them to the punch.
Because Stewart has already played for Hull and Charlton this season, he has to join Leeds on an initial 93-day loan after which point they will take him on a three-year deal.
McDermott said: "Cameron fits the bill as the type of player we are looking to recruit here. He has pace, he gives us something different, and he is hungry to do well."
"We were aware of Cameron's situation, and rules are rules. By joining us in this manner, it means we have a player who we know will be here for the next three and a half years, and we look forward to working with him for the long term."
Stewart's deal comes hot on the heels of Leeds agreeing terms with Crystal Palace for Jimmy Kebe.
Palace boss Tony Pulis has confirmed that Kebe is signing for Leeds, and said: "Kebe is on his way to Leeds as we talk. That'll be a loan until the end of the season. We'll be losing a few players."
Both Stewart and Kebe will be available for McDermott to make their debuts at Sheffield Wednesday on Saturday.