Daniel was a son of Johann I Bernoulli. Of all the Bernoulli family he was probably the most outstanding mathematician and certainly the one with the widest scientific interests. Daniel, who was born in Groningen in the Netherlands, studied at the universities of Basel, Strasbourg, and Heidelberg. His studies, which reflected his already wide interests, included logic, philosophy, and medicine in addition to mathematics.

In 1724 Daniel produced his first important piece of mathematical research – a work on differential equations, which sufficiently impressed the European scientific community to earn him an invitation to the St. Petersburg Academy of Sciences as a professor of mathematics. Once installed in Russia he continued to pursue his varied interests and obtained a post at the academy for his friend Leonhard Euler. In 1733 he left Russia to return to Switzerland to take up a chair in mathematics at Basel. Bernoulli's wide interests continued to occupy him and during his time at Basel he also held posts in botany, anatomy, physiology, and physics.

In Switzerland Daniel did the work for which he is best known, namely his virtual founding of the modern science of hydrodynamics using Isaac Newton's laws of force. He published these ideas in his Hydrodynamica (1738). Apart from his work in fluid dynamics Daniel made distinguished contributions to probability theory and differential equations in mathematics, and to electrostatics in physics. He also laid the basis for the kinetic theory of gases. Like his uncle, Jakob I Bernoulli, Daniel corresponded voluminously with many scholars throughout Europe, thus extensively disseminating his new ideas.