Wigan have announced Uwe Rosler as their new manager after agreeing compensation with Brentford.
Marseille have parted company with manager Elie Baup in the wake of Friday's defeat to Nantes at the Stade Velodrome.
The 28-year-old former Manchester City forward, son of Ian Wright and brother of Shaun Wright-Phillips, was released by Charlton at the end of last season.
"Since Bradley's potential was first recognised by Manchester City and the England Under-20s, he has proved to be a goalscorer of note," Red Bulls sporting director Andy Roxburgh told the franchise's official website.
"He'll add another dimension to our roster with his pace and technical ability."
Wright-Phillips also numbers Southampton and Plymouth among his former clubs and most recently played for Brentford, on loan from Charlton.