He was born in Helsinki, the son of a Professor of Engineering. He studied at Helsinki University from 1924, graduating in 1928 having studied under Ernst Lindelöf and Rolf Nevanlinna.
He assisted Nevanlinna in 1929 with his work on Denjoy's conjecture on the number of asymptotic values of an entire function. Ahlfors was appointed lecturer in mathematics at the University of Turku. He completed his doctorate in 1930.
In 1935 he went to Harvard University and in 1936 he was one of the first to be awarded the Fields Medal. He returned to Finland in 1938 to take up a post at the University of Helsinki, but the outbreak of war led to problems although Ahlfors was unfit for military service. He was offered a post at the Federal Polytechnic Institute at Zurich in 1944 and finally managed to travel there in March 1945. He did not enjoy his time in Switzerland and jumped at a chance to leave, returning to work at Harvard where he remained until he retired in 1977; he was William Caspar Graustein Professor of Mathematics from 1964. He was awarded the Vihuri Prize in 1968 and the Wolf Prize in Mathematics in 1981.
His book Complex Analysis (1953) is still the standard text for most courses on the topic. Ahlfors wrote several other significant books, including Riemann surfaces (1960) and Conformal invariants (1973).