The 3,600-passenger vessel is the largest cruise ship designed for the British holiday market, operator P&O has said.
Its home port will be Southampton for the summer months, after being built in Italy at a cost of almost £0.5bn.
The ceremony, which Prince Philip also attended, started at about midday and marked the fifth official naming of a cruise ship by Her Majesty.
Captain Paul Brown, who gave the Queen a tour of the ship, said: "It is my great honour after 33 years at sea to show the Queen around.
"I will be showing her the atrium and the bridge then heading down to the restaurant for lunch."
Britannia bears the same name as the Queen's former Royal Yacht Britannia, which was decommissioned in 1997 after more than 40 years of service.
The 141,000-tonne ship features a 94m (308ft) union jack on its bow and will make its maiden voyage to Spain, Italy and France on 14 March.
At 330m (1,082ft), the ship is longer than the Shard is tall.
British Brut NV from the Wiston Estate Winery at Pulborough in West Sussex is being used for the naming ceremony in Britannia's home port of Southampton.
Source : HKSG.