Beck was born in England in 1749. He was employed as an instructor in mathematics at Woolwich from 1776, but was afterward dismissed. He emigrated to the United States in 1795, and was employed in painting pictures. One of his paintings, The Great Falls of the Potomac (1796) was purchased by President George Washington. Washington hung the painting in his parlor at Mount Vernon, where it remains today.
Beck also wrote short poems, made poetic translations from Anacreon, Homer, Virgil, and Horace, and in 1812 published Observations on the Comet.
The obituary of Beck published in The Kentucky Gazette eulogized his nature paintings as one of the best among the works of the contemporary artists. The talented artist, however, was hardly given any credit for his outstanding works and was driven in his later days to a life of drudgery at the school he was running, frustration and bitterness.
Although Beck failed to command the respect and recognition, so deserving of him in his life career, his paintings of wild nature and western landscapes, "The Potomac River Breaking through the Blue Ridge and "The Great Falls of the Potomac" purchased by George Washington in 1797 put his work on high esteem. His depiction of the western landscape around the Potomac River in those paintings showcased life in its fullest bloom and divinity. The sheer power and force of those paintings so much influenced Washington that a good number of Beck's classic large paintings adored the walls of the New Room on the eastern side of Mount Vernon.