Guldberg was educated at the university in his native city of Christiania (now Oslo) and started his career teaching at the Royal Military School there in 1860. He was appointed to the chair of applied mathematics at the university in 1869.

Guldberg's main work was on chemical thermodynamics. In 1863 he formulated the law of mass action in collaboration with his brother-in-law, the Norwegian chemist Peter Waage (1833–1900). The law states that the rate of a chemical change depends on the concentrations of the reactants. Thus for a reaction: A + B → C the rate of reaction is proportional to [A][B], where [A] and [B] are concentrations. Guldberg and Waage also investigated the effects of temperature. They did not gain full credit for their work at the time, partly due to their first publishing the law in Norwegian. However, even when published in French (1867) the law received little attention until it was rediscovered by William Esson and Vernon Harcourt working at Oxford University.

In 1870 Guldberg investigated the way in which the freezing point and vapor pressure of a pure liquid are lowered by a dissolved component. In 1890 he formulated Guldberg's law. This relates boiling point and critical temperature (the point above which a gas cannot be liquefied by pressure alone) on the absolute scale. The law was discovered independently by Phillippe-Auguste Guye.