Trippe was born in Sea Bright, New Jersey, on June 27, 1899, the great-great-grandson of Lieutenant John Trippe, captain of the USS Vixen.
Trippe attended the Bovea School and graduated from The Hill School in 1917.
He enrolled at Yale University but left when the United States entered World War I to apply for flight training with the United States Navy. After completing training in June 1918, he was designated as a Naval Aviator and was commissioned as an Ensign in the United States Navy Reserve.
Trippe was treasurer at the first meeting of the National Intercollegiate Flying Association in 1920.
The end of World War I precluded him from flying in combat. After he Demobilized from active duty, he returned to Yale, graduating in 1921.
After graduation from Yale, Trippe began working on Wall Street, but soon became bored. In 1922 he raised money from his old Yale classmates, selling them stock in his new airline, an air-taxi service for the rich and powerful called Long Island Airways.
Once again tapping his wealthy friends from Yale, Trippe invested in an airline named Colonial Air Transport, which was awarded a new route and an airmail contract on October 7, 1925.
Interested in operating to the Caribbean, Trippe created the Aviation Corporation of the Americas. Based in Florida, the company would evolve into the unofficial United States flag carrier, Pan American Airways, commonly known as Pan Am.
Pan Am's first flight took off on October 19, 1927, from Key West, Florida, to Havana, Cuba, in a hired Fairchild FC-2 floatplane being delivered to West Indian Aerial Express in the Dominican Republic.
Trippe married Elizabeth "Betty" Stettinius Trippe (1904–1983), the sister of United States Secretary of State Edward R. Stettinius Jr., in 1928.
Trippe was a member of The Royal and Ancient Golf Club of St Andrews in Scotland and president of the Maidstone Club in East Hampton, New York, from 1940 to 1944.
Trippe quickly recognized the opportunities presented by jet aircraft and ordered several Boeing 707 and Douglas DC-8 airplanes. Pan Am's first scheduled jet flight was operated on October 26, 1958 by 707 Clipper America out of Idlewild International Airport (now JFK) to Le Bourget Airport, Paris. The new jets allowed Pan Am to cut the flight time nearly in half, introduce lower fares, and fly more passengers in total.
In 1965, Trippe received the Tony Jannus Award for his distinguished contributions to commercial aviation.
Trippe gave up the presidency of the airline in 1968. He continued to attend meetings of the board of directors and maintained an office in the company's Park Avenue office building.
Trippe suffered a stroke in September 1980, which forced him to cut back on his workload; he died after suffering a second stroke at his New York City home on April 3, 1981, at the age of 81. He is buried in Green-Wood Cemetery in Brooklyn.