The "after-hours" events, modelled on similar programmes at the Tate Modern and V&A Galleries in London, are aimed at attracting a younger, hipper crowd to the museum, which will fully reopen next month after a 46.4 million overhaul.
The year-long RBS Museum Lates series, to be launched in the autumn, will mainly take place in the newly-restored grand gallery of the Victorian-era Royal Museum building, which has been closed for three years.
RBS said the revamp would turn the attraction into "one of the world's great museums".
Among the new events will be live music performances, one-off art displays and installations, cutting-edge fashion catwalk shows and design showcases.
The museum plans to lure a whole new audience to the building - which dates back to 1861 - by promoting the events through digital programmes and social networking sites such as Facebook and Twitter. Celebrity speakers and performing artists will also be lined up in a bid to create "hot-ticket" events.
The museum has already dipped a toe into such initiatives, having held a late-night event during a hugely popular exhibition devoted to animation studio Pixar several years ago.
Officials at National Museums Scotland (NMS), which runs the attraction, have previously said they wanted to use the building outwith normal opening hours. In the past it has been opened in the evening only for gala dinners and corporate banquets.
The Edinburgh International Festival has already snapped up the grand gallery for a series of late-night Indian music nights in August.
An NMS spokeswoman said: "The spectacular redevelopment of the museum provides an opportunity to expand the range of events we offer alongside dramatic new displays. This is the first in a series of innovative programmes that will inspire and engage new audiences.
"Our collections celebrate huge achievements in the arts, culture, business and science worldwide and the legacy of Scots who were driven by a passion for exploration, discovery and invention."
The RBS sponsorship agreement comes just weeks after the bank struck a lucrative new deal with tennis star Andy Murray.
RBS has been forced to make cutbacks since its taxpayer-funded bail-out, although its backing of rugby's Six Nations Championship was spared and last year it renewed a deal to back the Royal Highland Show. It also unveiled a new sponsorship deal with Scottish Rugby in December.
However, the bank ended its long relationship with the Edinburgh Festival Fringe last year.
Sir Philip Hampton, chairman of the RBS Group, said: "We're delighted to be joining forces with National Museums Scotland. RBS has a great heritage going back almost 300 years, so it is natural that we should be supporting this great institution.
"The redevelopment of the museum will transform this wonderful Scottish asset into one of the world's great museums and we're very proud to be a partner."