The 20-year-old Robson has signed a new two-year contract.
Manager Csaba Laszlo said: “I am happy Jamie has signed another contract with the club. I believe he has the potential to go and play at a higher level, but he also has some learning still to do.
“This news is good for the club as he can help us achieve our goals and for Jamie who can continue his development and fulfil his potential at the club where he broke through.”
Robson made his United debut in September 2015 and has played 68 times, scoring two goals.
His deal comes after United confirmed goalkeeper Deniz Mehmet has extended his contract at the club into next season.
Midfielder Fraser Fyvie has also signed a new two-year deal to stay at Tannadice.
