Bloembergen was born in Dordrecht on March 11, 1920, where his father was a chemical Engineer and executive. He had five siblings, with his brother Auke later becoming a legal scholar. In 1938, Bloembergen entered the University of Utrecht to study physics. However, during World War II, the German authorities closed the University and Bloembergen spent two years in hiding.

Bloembergen left the war-ravaged Netherlands in 1945 to pursue graduate studies at Harvard University under Professor Edward Mills Purcell. Through Purcell, Bloembergen was part of the prolific academic lineage tree of J. J. Thomson, which includes many other Nobel Laureates, beginning with Thomson himself (Physics Nobel, 1906) and Lord Rayleigh (Physics Nobel, 1904), Ernest Rutherford (Chemistry Nobel 1908), Owen Richardson (Physics Nobel, 1928), and finally Purcell (Physics, Nobel 1952). Bloembergen's other influences include John Van Vleck (Physics Nobel, 1977) and Percy Bridgman (Physics Nobel, 1946).

Bloembergen returned to the Netherlands in 1947, and submitted his thesis Nuclear Magnetic Relaxation at the University of Leiden. This was because he had completed all the preliminary examinations in the Netherlands, and Cor Gorter of Leiden offered him a postdoctoral appointment there. He received his Ph.D. degree from Leiden in 1948, and then was a postdoc at Leiden for about a year.

Bloembergen met Huberta Deliana Brink (Deli) in 1948 while on vacation with his school's Physics Club. She was able to travel with Bloembergen to the United States in 1949 on a student hospitality exchange program; he proposed to her when they arrived in the States, and were married by 1950 on return to Amsterdam. They were both naturalized as citizens of the United States in 1958. They had three children.

In 1949, he returned to Harvard as a Junior Fellow of the Society of Fellows. In 1951, he became an Associate Professor; he then became Gordon McKay Professor of Applied Physics in 1957; Rumford Professor of Physics in 1974; and Gerhard Gade University Professor in 1980. In 1990 he retired from Harvard.

By 1960 while at Harvard, he experimented with microwave spectroscopy. Bloembergen had modified the maser of Charles Townes, and in 1956, Bloembergen developed a crystal maser, which was more powerful than the standard gaseous version.

With the advent of the laser, he participated in the development of the field of laser spectroscopy, which allows precise observations of atomic structure using lasers. Following the development of second-harmonic generation by Peter Franken and others in 1961, Bloembergen expanded on the study of the theoretical study of nonlinear optics, the analysis of how photons in high-intensity electromagnetic radiation interact with matter. In reflection to his work in a Dutch newspaper in 1990, Bloembergen said: "We took a standard textbook on optics and for each section we asked ourselves what would happen if the intensity was to become very high. We were almost certain that we were bound to encounter an entirely new type of physics within that domain".

In addition, Bloembergen served as a visiting professor. From 1964 to 1965, Bloembergen was a visiting professor at the University of California, Berkeley. In 1996–1997, he was a Visiting Scientist at the College of Optical Sciences of the University of Arizona; he became a Professor at Arizona in 2001.

He was awarded the Lorentz Medal in 1978. He received the Bijvoet Medal of the Bijvoet Center for Biomolecular Research of Utrecht University in 2001.

Bloembergen shared the 1981 Nobel Prize in Physics with Arthur Schawlow, along with Kai Siegbahn. The Nobel Foundation awarded Bloembergen and Schawlow "for their contribution to the development of laser spectroscopy".

Bloembergen died on September 5, 2017, at an assisted living facility in his hometown Tucson, Arizona of cardiorespiratory failure, at the age of 97.

Six weeks before his arrival, Purcell and his graduate students Torrey and Pound discovered nuclear magnetic resonance (NMR). Bloembergen was hired to develop the first NMR machine. At Harvard he attended lectures by Schwinger, Van Vleck, and Kemble. Bloembergen's NMR systems are still in use currently in Medicine, where they are used to examine internal organs and tissues. Bloembergen’s research on NMR led to an interest in masers, which were introduced in 1953.