The 37-year-old joins New York from Brazilian club Vasco da Gama having previously played in the French league with Lyon.
A noted free-kick specialist, Juninho made 47 appearances for Brazil and was part of their squad in the 2006 World Cup finals.
"Juninho is a world-class player who our Global Sporting Director, Gerard Houllier, and I have known and admired for many years," said Red Bulls Sporting Director Andy Roxburgh.
"Aside from being a top dead-ball specialist and a tremendous talent, Juninho is a fantastic professional both on and off the field. He is in great physical shape and we think he can make a positive impact for us in 2013," he added.
Former Scotland manager Roxburgh has been over-hauling the Red Bulls squad recently and last week Mexican defender Rafa Marquez was allowed to join Mexican club Leon.
With former France and Arsenal striker Thierry Henry in attack and Australian ex-Everton midfielder Tim Cahill, the Red Bulls hope to make a real push for their first MLS title next season.
The club have yet to appoint a new head coach, however, after releasing Swede Hans Backe at the end of the season.
Local media reports have suggested the favourite for the job is former Scotland midfielder Gary McAllister, who was manager of English clubs Leeds United and Coventry City and worked with Houllier at Aston Villa.