Pełczyński studied mathematics from 1950 to 1956 at the University of Warsaw and received there his doctorate in 1958 under Stanisław Mazur with dissertation Własności izomorficzne przestrzeni Banacha związane ze słabą zbieżnością bezwarunkową szeregów (Isomorphic properties of Banach spaces with regard to unconditional convergence of series).[3] From 1967 to 2002 he worked at the Polish Academy of Sciences.
From 1967 onwards, he was a member of the editorial staff of the journal Studia Mathematica.
In 1966, Pełczyński was (with Boris Mityagin) an invited speaker at the International Congress of Mathematicians in Moscow.[5] In 1983, he was a plenary speaker at the International Congress of Mathematicians in Warsaw and gave the talk Structural Theory of Banach Spaces and Its Interplay with Analysis and Probability.