He will join up with his brother Bradley, who was the Red Bulls’ top scorer last season.
Wright-Phillips impressed Red Bulls sporting director Ali Curtis having trained with the MLS team after leaving QPR following their relegation from the Premier League in May.
Curtis told the Red Bulls website: “Shaun is a proven player who has played on soccer’s largest stage.
“He can play a number of positions for us and is an excellent fit in our locker room.
“When we evaluated the unique set of circumstances along with the quality that Shaun has, it became apparent that we needed to be aggressive about adding Shaun to our club.
“We are pleased that he will be wearing a Red Bull jersey and we can’t wait for him to take the field.”
Wright-Phillips will be available for the club’s visit to Philadelphia Union next weekend.
Head coach Jesse Marsch said: “We are pleased to add Shaun to our club.
“Shaun has performed at the highest levels of the game for his entire career, in the Premier League and on the international level, and brings a wealth of talent and experience.
“He has been training here and we have seen his professionalism day in and day out. We think he is a tremendous addition both on the field and as a veteran presence in our locker room.”