The British Museum will use the cash for a new show
The celebrated arts institutions will receive the sponsorship package, called Invest and Inspire, for two years beginning in November.
Additional elements of the deal include supporting entertainment and educational projects to encourage the public to go to the four venues.
Baroness Blackstone, minister of state for the arts, welcomed the sponsorship plans.
"Partnerships such as this offer exceptional opportunities for businesses to achieve far-reaching business objectives, to promote artistic excellence and innovation and to collaborate effectively in improving access to the arts for all," she said.
Barclays added that it hoped to inspire other businesses to support the arts in the same way.
The sponsorship plans will begin by supporting the new Olivier season at the National Theatre.
The National's outgoing director Trevor Nunn, who will be replaced by Nicholas Hytner in 2003, said he was "delighted" by the help being given to the state-funded theatre, one of the most respected in the UK.
The British Museum will receive financial support to stage an exhibition on the Queen of Sheba, beginning in June 2002.
Another exhibition, at the National Gallery, will receive money to put on a Titian exhibition in Spring 2003.
Big business
And Tate Britain will use the money to put on a Turner and Venice exhibition from October 2003 to January 2004.
Plans are already in place for the cash - with a public day planned on London's South Bank in conjunction with the National Theatre.
And a number of educational activities at each venue are also aimed at raising the community's appreciation and enjoyment of the arts.
The arts sponsorship package is latest deal in what is now considered big business among many big companies.
During the past five years, commercial investment in the arts has doubled, reaching a total of £150m during 1999-2000.
Benefits for companies include the chance to promote brands, entertain clients in the sponsored venues and build links with their local community.