She declared the building open with a broadcast on BBC Radio 4, and also visited BBC Radio 1 and the BBC newsroom.
The Queen said it was a "great pleasure" to declare the building open.
The Duke of Edinburgh had also been expected to attend, but was admitted to hospital on Thursday for an operation.
Crowds gathered outside the building, which is flying the Royal Standard, to await the arrival of the Queen, who is wearing a powder blue coat and hat.
BBC Trust chairman Lord Patten and BBC director general Lord Hall met the Queen and escorted her on the first part of her visit.
She started the tour, her first visit to the corporation's recently expanded headquarters, by visiting BBC Radio 1 and meeting presenters including Nick Grimshaw, Trevor Nelson and Sara Cox.
She then visited the station's famous Live Lounge to watch a live performance by The Script, whose lead singer is Danny O'Donoghue, also well-known as a judge on BBC One show The Voice.
Her next destination was the building's third floor, where Fran Unsworth, the BBC's acting director of news, introduced her to several BBC Radio 4 staff, including Today presenter John Humphrys.
She then joined another Today presenter, James Naughtie, and Sian Williams live on Radio 4 where she gave a short address to declare the BBC's new home open.
"I hope this new building will serve you well for the future and I am delighted to declare it open today," she said.
Afterwards, she met Huw Edwards and Sophie Raworth at the start of a tour of the BBC newsroom.
The guided tour took her to look through the glass during a News Channel broadcast, and staff in the building laughed and broke into a round of applause as she appeared in the background of the studio shot.
After leaving the basement-level newsroom she met people including David Dimbleby and Sir Bruce Forsyth in the ground-floor reception.
At the end of her visit, the Queen unveiled a plaque marking the occasion at a reception attended by BBC staff, presenters and trustees.
Before the plaque was unveiled, Lord Patten wished the Duke of Edinburgh a quick recovery from his operation.
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