Virgin Radio will continue in its present form until the autumn. During this period, TIML will develop a new music and entertainment brand, with Virgin Enterprises retaining the Virgin Radio brand as part of its own global radio strategy.
TIML will invest more than £15m in developing the new brand, which it claims will be faithful to its existing format.
SMG will receive another £8m for Virgin Radio, to become payable within two years of closing, if TIML gets the license to use the Virgin brand.
Richard Bransons's Virgin Group has objected to TIML using the brand because Bennett Coleman competes with the Hindustan Times Group, with which Virgin has a joint venture in India.
Branson, said: "Virgin Radio International will now go on to grow a truly global Virgin Radio brand over the airwaves and on the internet -- tying in with our other great music brands such as Virgin Festivals International -- bringing all that is unique about Virgin Radio to millions of listeners, not only in the UK where we are considering options to re-launch Virgin Radio on FM, but across the globe in the near future."
Mr A P Parigi, managing director and chief executive of TIML, said: "Now is a great period to be entering the UK market and the opportunity to acquire a valuable radio asset couldn't have come at a better time.
"We have worked with ARI for many years now and their experience and expertise, coupled with that of the award winning staff at Golden Square, will deliver our collective vision of a powerful and exciting new brand that will engage all key stakeholders."
SMG shares dropped 1.8% to 13.5p as of 9:24am in London trading, valuing the company at £128.5m. Before today, the stock had declined 15% this year.
The Scottish media company bought the station in 2000 for £225m from broadcaster Chris Evans' Ginger Media Group.
Other bidders for Virgin Radio included Global Radio and UTV, the Belfast-based TV and radio company that owns the UK's TalkSport, and Malaysian company Astro All Asia Networks backed by Malaysian billionaire Ananda Krishnan.