Born Morton Tecosky in Philadelphia, Pennsylvania, DaCosta began his career as an actor in the Broadway production of Thornton Wilder's The Skin of Our Teeth starring Tallulah Bankhead in 1942.
DaCosta had a string of hit Broadway productions in the 1950s: Plain and Fancy, No Time for Sergeants, Auntie Mame and The Music Man.
Additional Broadway directing credits include Sherry!, The Women, Saratoga, and Maggie Flynn.
DaCosta produced and directed the films Auntie Mame (1958), The Music Man (1962), and Island of Love (1963).
DaCosta, who was always known by his nickname Tec, died of heart failure in Redding, Connecticut.