Koksma received his Ph.D. degree (cum laude) in 1930 at the University of Groningen under supervision of Johannes van der Corput, with a thesis on Systems of Diophantine Inequalities. Around the same time, aged 26, he was invited to become full professor at the Vrije Universiteit Amsterdam. He accepted and in 1930 became the first professor in mathematics at this university. Koksma is also one of the founders of the Dutch Mathematisch Centrum (today Centrum Wiskunde & Informatica).
One of Koksma's main works was the book Diophantische Approximationen, published in 1936 by Springer. He also wrote several papers with Paul Erd?s.
Koksma had two brothers who were also mathematicians; Jan Koksma and Marten Koksma.