Leigh was born in Merced, California, and grew up in Merced. She was the only child of Helen Lita (née Westergaard) and Frederick Robert Morrison. Her birth name was Jeanette Helen Morrison. Her maternal grandparents were immigrants from Denmark. In winter 1945, she was discovered by actress Norma Shearer, whose late husband Irving Thalberg had been a senior executive at Metro-Goldwyn-Mayer.