His father died insolvent in 1742 and at about this time Greenwood apprenticed to Thomas Johnston, a Boston line engraver, sign painter, and japanner.

He settled there for a time to learn the art of making mezzotints, and was documented as a member of the Amsterdam Drawing Academy in 1758 by Jacob Otten Husly.

At the request of the Earl of Bute Greenwood made a journey, in July 1771, into Holland and France purchasing paintings; he afterwards visited the continent, buying up the collections of Count van Schulembourg and the Baron Steinberg.

One of Greenwood's best-known works is Sea Captains Carousing in Surinam (1755), a drunken scene featuring various prominent Rhode Island merchants, including Declaration of Independence signatory Stephen Hopkins, Governor Joseph Wanton, Admiral Esek Hopkins, and Governor Nicholas Cooke.

[3] In 1770, Greenwood wrote to his childhood friend, the painter John Singleton Copley, to commission a portrait of his mother Mary Charnock Devereux: ‘I am very desirous of seeing the good lady’s face as she now appears, with old age creeping upon her.’ this portrait is now part of the international painting collection at the Museum of New Zealand Te Papa Tongarewa.