Born in Edinburgh, Scotland, he studied graphic design at the Duncan of Jordanstone College of Art and Design in Dundee, as well as film and television at the Royal College of Art in London. In 1970, he moved to the United States with his wife Elizabeth. His peculiar style ended up attracting the attention of American and European fashion magazines. In 1975, Albert won a Grammy Award, and in 1976 he got his first assignment for Vogue. He has published many books and organized several personal exhibitions at many museums and galleries. Watson has also produced hundreds of successful advertising campaigns, as well as directed many TV commercials.
The industry magazine Photo District News has elected him among the 20 most influential photographers of all time. He has won several awards, including the Lucie Award, three ANDY Awards, the Centenary Medal of the Royal Photographic Society and a Grammy Award (for the cover of a Mason Proffit album).