At the age of thirteen he was apprenticed to one of his older brothers, Caleb Ashworth Tate (d. 1846), who was a grocer in Liverpool. Seven years later Henry set up on his own, by buying the business of Aaron Wedgwood in Old Haymarket, Liverpool. By the time he was thirty-six, Henry Tate had six shops—four in Liverpool, one in Birkenhead, and one in Ormskirk. He also expanded into the wholesale trade in 1857.
At the time of the move to London, Tate learned of a process for making sugar into small cubes.
He endowed a new gallery at Millbank in London. This became the National Gallery of British Art, but has always been far better known as the Tate Gallery. He donated sixty-five of his own pictures, and three sculptures to the gallery. They included many which reflected his conservative taste, such as Orchardson's Her First Dance and The First Cloud; Waterhouse's Lady of Shallot; Millais' Ophelia, Vale of Rest, and North-West Passage; and several by Tindeman, Reid, and—Queen Victoria's own favourite—Sir Edwin Landseer.
The building for the new gallery was designed by Sydney R. J. Smith, and opened by the prince of Wales on 21 July 1897.
Tate lived at Park Hill in Streatham and he is buried at West Norwood Cemetery.