The Normanton-born utility player will help fill the void left by the likes of his ex-Hull FC team-mate Danny Washbrook and Tim Spears both retiring.
Thompson, 30, started his career at Castleford Tigers where he also played briefly with current York head coach James Ford.
He scored 28 tries in 78 games for Castleford before joining Hull.
Thompson made more than 100 appearances for the Black and Whites and has just completed a second stint at Leigh, having also featured six times with Rhinos in 2018.
He has featured with York before, playing five times when just 18 years old and on loan from Castleford in 2011.
Ford, who has also signed Joe Brown, Jamie Ellis and Liam Harris for next season, said: “I’m absolutely delighted to get Jordy over the line.
“He’s a very competitive player with an outstanding skill set for a middle.
“Jordy will add a significant amount of tenacity to our team, something that I was very keen to add to our team and squad.”
Thompson, who started out as a three-quarter but now plays loose forward and prop, said: “I’m really happy to have joined the club.
“It’s a good club that is looking to push on to be one of the best in the division.
“It was quite an easy decision and, obviously, the facilities are second to none so I’m looking forward to it.”
The experience of working with Ford before also helped.
“That’s what made the decision to come and join easy for me, really,” said Thompson, who has amassed more than 250 career appearances.
“He was a big thing in that and, obviously, already having a good relationship with him, I think the rugby side will come from that and I’ll enjoy myself under him.”