Thomas Huckle Weller was born on June 15, 1915, in Ann Arbor, Michigan, where his father was chairman of the pathology department at the University of Michigan Medical School. Weller showed an interest in biology from an early age. He attended the University of Michigan for his bachelor's and master's degrees, then entered Harvard Medical School in 1936, where he studied parasitology. Weller did research under John Enders, who was then studying methods of growing animal cells outside the body.

While in medical school, Weller began working on tissue-culture techniques and also took up an interest in viruses that cause infectious diseases. After medical school, he began work at Children's Hospital in Boston, but this was soon interrupted by service in the Army Medical Corps during World War II. Because he was stationed in Puerto Rico, Weller worked on tropical diseases, such as one caused by the tropical liver parasite Schistosoma. After returning to Children's Hospital, he began perfecting ways of keeping cells alive by changing the medium instead of transferring the cells. He used this method to study the mumps virus, then began working on the varicella virus, which causes chickenpox.

Along with Enders and another colleague, Frederick C. Robbins (his roommate in medical school), Weller worked with the poliomyelitis virus, developing a technique that allowed them to grow a virus in culture for many generations. This method made it easier to eventually culture a variant, an attenuated virus that could multiply without being dangerous--the kind of virus that is ideal for a vaccine. Although Weller did not work on a polio vaccine (later developed by Jonas Salk and Albert Sabin), this lab technique enabled others to do so, earning Weller, Enders, and Robbins the 1954 Nobel Prize for physiology or medicine.

Weller began studying the virus that causes chickenpox and showed that it is the same virus that causes the skin disease known as shingles (herpes zoster). He also isolated cytomegalovirus, and in 1962, he isolated the virus that causes rubella (German measles).

Weller left Children's Hospital in 1954 and spent his subsequent years as chairman of Harvard's Department of Tropical Public Health. He married Kathleen Fahey in 1945; they have two sons and two daughters.