The forwards join Julius Randle, Bobby Portis, Taj Gibson, Elfrid Payton and Wayne Ellington as free agents who the Knicks hope will improve what was the NBA's worst team last season.
Morris averaged 13.9 points and 6.1 rebounds in 75 games last season for Boston, his fifth straight season scoring more than 10 points per game.
Bullock averaged 11.3 points while playing for Detroit and the Los Angeles Lakers.
Terms of the deals announced Tuesday were not disclosed.
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