Koopmans was born in 's-Graveland, Netherlands. He began his university education at the Utrecht University at seventeen, specializing in mathematics. Three years later, in 1930, he switched to theoretical physics. In 1933, he met Jan Tinbergen, the winner of the 1969 Nobel Memorial Prize in Economics, and moved to Amsterdam to study mathematical economics under him. In addition to mathematical economics, Koopmans extended his explorations to econometrics and statistics. In 1936 he graduated from Leiden University with a PhD, under the direction of Hendrik Kramers. The title of the thesis was "Linear regression analysis of economic time series".
Tjalling had two brothers, one of whom was theologist and reverend Dr Jan Koopmans, who, in 1940, early during the German occupation of the Netherlands, wrote the widely distributed pamphlet "Bijna te laat" ("Almost too late", 30,000 copies), warning about the Future of the Jews under the Nazi regime. In 1945, towards the end of the war, he witnessed an execution of hostages in Amsterdam from behind a window and was mortally wounded by a stray bullet.
Koopmans' early works on the Hartree–Fock theory are associated with the Koopmans' theorem, which is very well known in quantum chemistry. Koopmans was awarded his Nobel memorial prize (jointly with Leonid Kantorovich) for his contributions to the field of resource allocation, specifically the theory of optimal use of resources. The work for which the prize was awarded focused on activity analysis, the study of interactions between the inputs and outputs of production, and their relationship to economic efficiency and prices. Finally, the importance of the article by Koopmans (1942) deriving the distribution of the serial correlation coefficient was recognized by John von Neumann, and it later influenced the optimal tests for a unit root by John Denis Sargan and Alok Bhargava (Sargan and Bhargava, 1983).