Watt was born in Greenock and studied at Glasgow School of Art. She first came to prominence when, still a student, she won a national portrait competition organised by the National Portrait Gallery in London. Watt subsequently became known for her paintings of figures, often female nudes, in light-filled rooms. This led on to a series of works exploring the properties of fabric. In 2000 she became one of the youngest artists to have a solo exhibition at the Scottish National Gallery of Modern Art. Watt participated in the 2010 exhibition Autoritratte at the Sala delle Reali Poste in the Uffizi Gallery, Florence, Italy, which brought together female self-portraits from the sixteenth century to today. She was Associate Artist at the National Gallery, London in 2006–8. In 2008 she was awarded an OBE.