What years did the Celtics win NBA championships? The Celtics have won 16 NBA Championships: 1957, 1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1968, 1969, 1974, 1976, 1981, 1984, and 1986   ANSWER They actually wo…n 17 championships.