The company, which is 55 per cent owned by CDL Hotels, a Hong Kong hotel management group, adds the Britannia to its London portfolio of luxury hotels that includes the Gloucester, Bailey's Hotel, The Chelsea Hotel and the Copthorne Tara.
The Britannia has been valued at pounds 83m and made pounds 5.3m operating profits in 1995. Funding for the purchase will be drawn from Millennium's own resources.
Millennium's shares rose 3p to close at 318.5p. Its shares have risen almost 15 per cent since they began trading on 25 April.
The company said it would rebrand the Britannia as a Millennium property, denoting it a four-star deluxe hotel focused on the international business and leisure traveller.
After buying the Britannia, the company will own 16 hotels in Britain, three in France, two in Germany and three in New York - including a 42 per cent stake in the Plaza Hotel.
The company, which recently reported a 53 per cent increase in first- half pre-tax profits to pounds 15.1m, said selective acquisitions were an important step in its growth strategy.
Peter Taylor, director of UK operations, said: "London, other than where we're located now, is obviously of interest." A tourist boom and a room shortage in the capital is fuelling demand. Occupancy rates this summer hit their highest levels in a decade at 82.5 per cent.
The company is also looking at other locations including Europe and North America.