The Australian forward has signed a one-year contract with the Betfred Championship club after six seasons at Leeds.
The Yorkshire Evening Post revealed earlier this month that York and Bradford Bulls were both chasing the ball-handling front-rower.
Cuthbertson, 35, joined Rhinos ahead of the 2015 season and was a Man of Steel nominee that year when they won the treble of Challenge Cup, league leaders’ shield and Super League title.
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He was a Super League champions again two years later and has made two starts and nine substitute appearances for Rhinos in 2020.
He also had a successful two-year spell as coach of Rhinos' women's side, winning the Challenge Cup twice, league leaders' shield and Grand Final.
Cuthbertson will join big-name recruits Ryan Atkins and Danny Kirmond - both signed from Wakefield Trinity - at York next season.
He said: “I’m very excited.
“I’ve had a good couple of conversations with [owner] Jon Flatman) and Fordy [coach James Ford] about what they’re aiming to achieve next year; it’s very exciting and I think it’s a great opportunity.
“The fact that York as a team represents such a big city makes it a great opportunity to help the game grow and, hopefully, find our way into Super League.”
Ford said Cuthbertson - whose signing has been funded with help from York fans and sponsors - “will make a significant impact on our preparations and culture, as well as our on-field performances”.
He insisted: “He gives us added leadership and experience, but also a different dimension to our attack with his offload game.
“I was impressed with Adam’s drive to be the best version of himself, his humility and I’m excited to work with him.”
Cuthbertson has played 154 games for Rhinos, scoring 36 tries.
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