The deal gives the Suns a third forward in their attempt to replace free agent Amare Stoudemire. Phoenix signed swingman Josh Childress in a sign-and-trade deal with Atlanta earlier Wednesday and picked up Hakim Warrick in similar swap with Chicago.
Turkoglu spent one disappointing season in Toronto, averaging 11.3 points after being named the NBA's most improved player with Orlando the year before.
Barbosa, the NBA's 2006-07 sixth man of the year, played seven seasons in Phoenix, averaging 12.6 points as a key sub. Jones spent most of last season in the NBA Developmental League.