The last-minute sale, for an undisclosed amount, means that they have now been withdrawn from today's auction at Christie's of unique polar memorabilia and will remain in Britain.
The Museum director, Richard Ormond, said: "We are grateful to the Scott and Shackleton families for allowing items to be bought for the nation. We are grateful to Christie's for their help in facilitating the sale for the nation."
Museum officials set up a campaign to keep the relics in Britain, fearing they would be sold abroad. Scott's silk sledging flag features in photographs of the expedition team taken at the South Pole.