He was educated at Warsaw University. In 1905, after the closure of the University by the Russians, he moved to Göttingen and in 1906 to the Pulkowa Observatory. He also worked at the Engel'gardt Observatory at Kazan University from 1910–1915; in Russian his last name was written Банахевич.
In 1919, after Poland regained her independence, Banachiewicz moved to Kraków, becoming a professor at the Jagiellonian University and the director of Kraków Observatory. He authored approximately 180 research papers and modified the method of determining parabolic orbits. In 1925, he invented a theory of "cracovians" — a special kind of matrix algebra — which brought him international recognition. This theory solved several astronomical, geodesic, mechanical and mathematical problems.
In 1922 he became a member of PAU (Polska Akademia Umiejętności) and from 1932 to 1938 was the vice-president of the International Astronomical Union. He was also the first President of the Polish Astronomical Society, the vice-president of the Geodesic Committee of The Baltic States and, from 1952 to his death, a member of the Polish Academy of Sciences. He was also the founder of the journal Acta Astronomica. He was the recipient of Doctor Honoris Causa titles from the University of Warsaw, the University of Poznań and the University of Sofia in Bulgaria.