In a significant move in the NRL player market, Robson told Cowboys officials on Friday he would not re-sign beyond the end of next season.
Robson's decision is expected to lead to him linking with the Roosters, who have a known interest in the 26-year-old.
The Cowboys had only been willing to offer Robson a deal of around two-to-three years, while the Roosters are expected have put forward a four-year offer.
"We tabled our best possible offer, but unfortunately were not able to compete with the final offer Reece received," Cowboys football boss Micheal Luck said.
"Reece now has a young family and we respect his decision.
"He will continue to be an important member of our squad for 2025 and we look forward to his contributions in his final season at the club."
Robson's decision is likely to have ongoing ramifications in the NRL.
If signed by the Roosters, it will almost certainly spell the end of Brandon Smith's time at the NRL club.
Smith has previously indicated he is not interested in returning to the Cowboys, who he played under-20s with.
The Kiwi is off-contract at the Roosters at the end of 2025, having endured an at-times turbulent two seasons at the NRL club.
The news also comes after the Tri-colours confirmed a one-year extension for James Tedesco through until the end of 2026 on Friday.
Tedesco's signature gives the Roosters some much-needed stability in their senior playing group, after the mass exodus of long-time stalwarts at the end of 2024.
The deal means he will stay at the club until at least just before his 34th birthday, with the fullback seemingly happy taking year-by-year contracts.
"The Roosters have been my home for the past seven years, and I'm excited to continue playing for this incredible club," Tedesco said.
 "I'm proud to represent the Roosters and there's a strong bond among the group, so I'm looking forward to what we can achieve together in 2025 and beyond."
Tedesco is expected to remain at fullback for the entirety of the next two years, with coach Trent Robinson adamant last month there was no need to rush in future planning at No.1.
It came as the Roosters opted against any real pursuit of Melbourne star Ryan Papenhuyzen, who has also decided to stay with the Storm for 2026.
Halfback Sam Walker has also extended at the Roosters until the end of 2027 this summer, in a crucial few months for the club off the field.
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