Leopold Kronecker was born in Liegnitz, Prussia (now Legnica, Poland) into a Jewish family. In 1845, Kronecker wrote his dissertation at the University of Berlin on number theory, giving special formulation to units in certain algebraic number fields. Peter Gustav Dirichlet was his teacher.

After obtaining his degree, Kronecker managed the estate and business of his uncle, producing nothing mathematical for eight years. In his 1853 memoir on the algebraic solvability of equations, Kronecker extended the work of Évariste Galois on the theory of equations. He accepted a professorship at Friedrich-Wilhelms University (today: Humboldt University) of Berlin in 1883.

Kronecker also contributed to the concept of continuity, reconstructing the form of irrational numbers in real numbers. In analysis, Kronecker rejected the formulation of a continuous, nowhere differentiable function by his colleague, Karl Weierstrass. In an 1850 paper, On the Solution of the General Equation of the Fifth Degree, Kronecker solved the quintic equation by applying group theory (though his solution was not in terms of radicals, since this was already proven impossible by Abel–Ruffini theorem).

Kronecker's finitism made him a forerunner of intuitionism in foundations of mathematics.

Named for Kronecker are the Kronecker limit formula, Kronecker delta, Kronecker symbol, Kronecker product, Kronecker–Weber theorem, Kronecker's theorem in number theory, and Kronecker's lemma. He was the supervisor of Kurt Hensel, Adolf Kneser, Mathias Lerch, and Franz Mertens, amongst others.

Kronecker died on December 29, 1891 in Berlin. He is buried in the Alter St Matthäus Kirchhof Cemetery in Berlin-Schöneberg, close to Gustav Kirchhoff.