He was born in Charlestown, Massachusetts and graduated from Yale University, in 1810. Early in life he devoted himself to art and became a pupil of Washington Allston, a well-known American painter. Morse later accompanied Allston to Europe in 1811.
When studying in Rome in 1830, he became acquainted with the Danish sculptor Bertel Thorvaldsen; the two artists would sometimes take a walk together at night among the ancient ruins. Morse also painted Thorvaldsen's portrait.
In the 1850s, Morse came to Copenhagen and visited the Thorvaldsen Museum, where the sculptor's grave is in the inner courtyard. He was received by King Frederick VII, and he expressed his wish to donate his portrait from 1830 to the King. The Thorvaldsen portrait today belongs to Queen Margaret II of Denmark.
In the 1830, Morse had invented the electrical telegraph, based on Hans Christian Ørsted's discovery in 1820 of the relationship between electricity and magnetism. Morse also authored the Morse code signalling alphabet.
On February 8, 1838 Morse first publicly demonstrated the electrical telegraph to a scientific committee at the Franklin Institute in Philadelphia, Pennsylvania. In 1844 Morse sent the telegraph message "What hath God wrought?" from Washington, DC to Baltimore, Maryland
He died at his home at 5 West 22nd Street, New York, New York at the age of eighty-one, and was buried in the Green-Wood Cemetery in Brooklyn, New York.