The 44-year-old former lawyer was appointed head of the Scottish National Party (SNP) last week, taking over from outgoing leader Alex Salmond, whom she said she owed "a personal debt of gratitude".
Salmond's deputy for around 10 years, Sturgeon was the only candidate in the running to succeed him.
Addressing the Scottish Parliament in Edinburgh she made a "heartfelt" pledge to be "First Minister for all of Scotland".
"Regardless of your politics or your point of view, my job is to serve you. And I promise that I will do so to the best of my ability," she said yesterday, as supporters and family members watched from the chamber gallery.
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She made it clear that feminist issues would be high on her agenda, vowing to improve childcare and tackle pay inequalities.
"To become First Minister is special and a big responsibility. To make history as the first woman First Minister is even more so," she added.
"I hope that my election as First Minister does indeed help to open the gate to greater opportunity for all women. There should be no limit to your ambition or what you can achieve.
The nationalist leader said she would continue to fight for independence for Scotland despite her party's defeat in a referendum in September.
Since the vote, the SNP has been gaining in support and the British government has promised to grant Scotland sweeping new autonomous powers.
Prime Minister David Cameron congratulated Sturgeon on her appointment in a telephone call yesterday, according to a statement issued by his Downing Street office.
"The Prime Minister said he was looking forward to working with the new First Minister to address the opportunities and challenges facing Scotland and the UK as a whole," said a Number 10 spokesman.