Hudson was born in Devon in 1701. His exact birthplace is unknown. He studied under Jonathan Richardson in London and against his wishes, married Richardson's daughter at some point before 1725.
Hudson was most prolific between 1740 and 1760 and, from 1745 until 1755 was the most successful London portraitist.
He had many assistants, and employed the specialist drapery painter Joseph van Aken. Joshua Reynolds, Joseph Wright and the drapery painter Peter Toms were his students.
Hudson visited the Low Countries in 1748 and Italy in 1752. In 1753 he bought a house at Cross Deep, Twickenham, just upstream from Pope’s Villa. He retired toward the end of the 1750s. William Hickey described the elderly Hudson, "His figure was rather grotesque, being uncommonly low in stature, with a prodigious belly, and constantly wearing a large white bushy periwig. He was remarkably good tempered, and one of my first-rate favourites, notwithstanding that he often told me I should certainly be hanged.". He died at Twickenham in 1779. His extensive private art collection was sold off in three separate sales.