The 1962–63 FIBA European Champions Cup was the sixth season of the European top-tier level professional basketball club competition FIBA European Champions Cup (now called EuroLeague).

It was won by CSKA Moscow, after they beat Real Madrid in a three-legged EuroLeague Finals, after the two first games ended with an aggregate two-legged tie.

European national domestic league champions, plus the then current FIBA European Champions Cup title holders only, playing in a tournament system.

*series decided over one game in Casablanca.

First leg Fiesta Alegre fronton;Attendance 5,000, 23 July 1963[1] Second leg Lenin Palace of Sports;Attendance 20,000, 31 July 1963[1] *Third leg Lenin Palace of Sports;Attendance 20,000, 1 August 1963, Moscow, Soviet Union[1]