Greiner was born in Budapest, Hungary. His parents subsequently moved to Vienna before arriving in Australia in the early 1950s. He was educated at St Ignatius' College, Riverview in Sydney's lower north shore, before graduating with honours in Economics at the University of Sydney. Later he attended Harvard Business School. After briefly working for an Idaho timber company, Greiner returned to Australia, where he joined the timber company that his family owned. Greiner has also held the position of Australian chairman of British American Tobacco.
Political career
A member of the Liberal Party of Australia, Greiner unsuccessfully sought to enter the New South Wales Legislative Assembly for the safe Liberal seat of Willoughby in 1978. He defeated sitting member Laurie McGinty for Liberal preselection. Although defeated in his first bid to enter the legislature by local bus driver Eddie Britt as part of the "Wranslide" Labor victory that year (largely due to McGinty running as an independent), Greiner successfully contested a 1980 by-election for the electorate of Ku-ring-gai.