Hay was born in Scotland, but moved to Australia at the age of fourteen with his family. In 1978, Hay met Ron Strykert and the men began playing acoustic music as a duo. Soon after, Hay and Strykert became the band Men at Work after the addition of Jerry Speiser, John Rees and Greg Ham. The group released their debut album Business as Usual in 1981.
Following the breakup of Men at Work in 1985, Hay released several major label solo albums, including Looking for Jack (Columbia) and Wayfaring Sons (MCA), to some commercial success. He later became part of Ringo Starr's Seventh All-Starr Band.