Greene replaces Steve McLaughlin, who recently became chief commercial officer for digital and consumer revenues, and will report directly to chief executive Murdoch MacLennan.
He said: "I am delighted to be returning to the newspaper industry and joining the UK's biggest selling quality newspaper. I am looking forward to working with the promotions and circulation teams at the TMG."
Greene was at the INM from 1998 to 2008, where he devised the circulation and marketing strategy for the launch of the compact edition of The Independent. He also introduced learning-based promotions and achieved record sales uplifts for the paper.
He previously worked on a wide range of magazine titles as the circulation director for IPC Magazines and set up his own sales promotion agency LOAF Marketing after leaving INM.