Mittag-Leffler studied in Paris under Charles Hermite (Hermite, Charles) and in Berlin under Karl Weierstrass (Weierstrass, Karl), and in 1872 he became a lecturer in mathematics at the University of Uppsala, Sweden. Five years later he was appointed a professor of mathematics at the University of Helsinki, Finland. In 1881 he became a professor of mathematics at the University of Stockholm. With the financial patronage of King Oscar II of Sweden, he founded the journal Acta Mathematica in 1882, set up an editorial staff from the four Scandinavian countries, and served as chief editor for the next 45 years. To launch the journal, he attracted substantial contributions from the French mathematician Henri Poincaré (Poincaré, Henri), and in the early volumes he demonstrated his support for Georg Cantor (Cantor, Georg)'s work in set theory by publishing French translations of Cantor's papers (which had been originally published in German). In 1883 Mittag-Leffler secured a position at the University of Stockholm for the Russian mathematician Sofya Kovalevskaya (Kovalevskaya, Sofya Vasilyevna) (the first woman to achieve such a post in modern Europe). He was dedicated to the internationalization of mathematics and actively promoted international mathematical congresses.

Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus, analytic geometry, and probability theory). He worked on the general theory of functions, concerning relationships between independent and dependent variables. His best-known work concerned the analytic representation of a single-valued function; this work culminated in the Mittag-Leffler theorem, one of the basic theorems in analytic function theory. His estate and his mathematical library now form part of the Mittag-Leffler Mathematical Institute at Djursholm, Sweden.