Duffy said: "Andrew [Motion] hasn't had his yet so I've asked for mine up front."
Prime Minister Gordon Brown said: "She is a truly brilliant modern poet who has stretched our imaginations by putting the whole range of human experiences into lines that capture the emotions perfectly."
Culture Secretary Andy Burnham said Duffy "has achieved something that only the true greats of literature manage".
"That is to be regarded as both popular and profound," he said.
The reigning monarch chooses the Laureate on the advice of the government.
Carol Ann Duffy on her sexuality and rumours she was rejected last time for it
Part of Duffy's responsibilities over the next 10 years will be to write works commemorating royal events, a role her predecessor, Motion, has said he found "very difficult".
After being passed over for the Laureate job in 1999, she commented: "I will not write a poem for Edward and Sophie. No self-respecting poet should have to."
But speaking on Friday, she said: "Poetry is all about looking at the ordinary and transforming it - the Midas touch. And the monarchy has that too.
"The presence of the Queen can help heal, transform and make things magic," she added.
Fellow poet Roger McGough said there was a guarantee with Duffy that, in her commissioned poetry, "we get things which are real and surprising".
Archive interview with Carol Ann Duffy
Reports suggested Duffy was ruled out of the running for the Laureate post in 1999 because it was thought her sexuality might not play well in Middle England.
Asked on Woman's Hour if she was apprehensive about intrusion into her personal life, she said: "I am a very private person and will continue to protect my privacy and my daughter."
"When giving public readings I will be, as I always have been, accessible."
Her first themed collection, The World's Wife, spoke of great men, myths and moments in history through the women in the background. It included poems called Mrs Midas and Queen Kong.
In 2002 she was made a CBE.
The poet's work is taught in schools at GCSE and AS level.
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