Dudley was born at Johnson Hall, Eccleshall, Staffordshire during the American Revolution to Loyalist parents.

[1] In November 1775, his father had abandoned his office at Newport and sought refuge on board a British ship of war.

[1] Near the beginning of the nineteenth century, Dudley worked as a clerk in a counting room and made voyages from New York to the East Indies as a supercargo.

He joined the Albany Regency, the coterie which Martin Van Buren formed to lead the Bucktails, the group which fought DeWitt Clinton for control of New York's Democratic-Republican Party.

When Van Buren resigned his seat in the United States Senate to become Governor of New York in 1829, Dudley was elected to fill the vacancy.

[1] Dudley retired at the end of his term and spent the rest of his life in Albany, retaining his interest in politics as Jackson, Van Buren and others worked to form the Democratic Party after the Democratic-Republicans split in 1824, depending on which presidential candidate they supported.