The hotel has been on the market for three years and RBS originally sought £700m for the Park Lane property.
However, two previous auctions had failed before the Sahara India Pariwar group entered the deal, which was completed on 30 December.
Sahara Group’s chairman Subrata Roy Sahara said the acquisition was part of "major expansion plans" for the group.
"We are extremely happy to announce Grosvenor House joining the Sahara family," he said. "In addition to the acquisition of Grosvenor House, London will be the gateway for Sahara to introduce some of its new business ventures, internationally."
The JW Marriott-run hotel features 420 rooms, 74 suites and 4,000sqm of meetings space spread over 27 rooms.
The hotel’s largest meeting room is 1,779sqm and can accommodate 2,000 delegates.
The acquisition was brokered by Richard Lewczynski of Blandford Goldsmith and the plan is for Sahara to jointly manage the hotel with Marriott.
RBS representative Michael Strachan told C&IT: "We are generally looking at reducing our commercial real estate exposure."
The banking group has a further six hotels for sale - Hilton Brighton, Glasgow, Glasgow Grosvenor, Manchester Airport, Warwick and St Annes Bracknell.