He first lived in Western Australia between 1967 and 1974, where he worked as a manager for the Pastoralists and Graziers Association (PGA).
After a period working for a construction industry peak organisation in South Australia, he returned to Western Australia in 1978, working in industrial relations roles for the Confederation of Western Australian Industry.
Greig entered parliament at the 1987 Darling Range by-election, caused by the resignation of George Spriggs.
He attempted to transfer to the seat of Helena at the 1989 state election, but was defeated by the sitting Labor member, Gavan Troy.
After leaving office, Greig worked as a management consultant to various mining companies, and also developed a lavender farm in Mumballup (south of Collie).