The Catalans Dragons halfback will wind up with the French club at the end of the year, but will just make the short trip across the English Channel to link up with Hull KR on a two-year deal.
It means May, who is now 27 years old, will ply his trade for the English club during at least the 2024 and 2025 seasons.
May, who can play almost anywhere on the field in addition to the halves, has played 37 games for the Dragons since arriving at the start of the 2022 season, having previously spent five seasons in the Penrith Panthers' set-up where he played in two grand finals.
Hull KR head coach Willie Peters said May had been on the club's radar for a while.
"Tyrone (May) has been a player on our radar for a while. He's been really dominant in Super League over the last two seasons. We were looking to bolster our spine with some more experience and Tyrone will definitely bring that," Peters said.
"Tyrone's played in the big games and finals. He's been part of such a successful club like Penrith and he's doing wonderful things in Catalans, I'm looking forward to having his experience and knowledge with us next year to help us mentor our younger guys.
"He can play standoff, half back, centre and loose forward, Tyrone's versatility is going to be great for us but we're looking for him to cement a spot in our halves."
The half will join Peta Hiku in arriving at Hull next year as the Robins revamp their spine - it's believed the Cowboys' back will take the number one jersey after Lachlan Coote elected to retire earlier this year.
Other ex-NRL players in the Robins' squad include Rhys Kennedy, Tom Opacic, Sauaso Sue, Kane Linnett and Brad Schneider, while English international-considered players Ryan Hall and Ethan Batchelor are also at the club.