(BBC) Ms sturgeon has joined the list of women leaders to hold top positions in government as she is the first woman in Scotland to become a minister.
Ms Sturgeon, who succeeds Alex Salmond, said she had "big boots" to fill but would "wear them in my own way".
The politician, who is the first woman to hold the job, took over as SNP leader from Mr Salmond at the weekend.
Speaking in the Scottish Parliament, Ms Sturgeon pledged to be first minister "of and for all of Scotland".
She said: "A first minister who will always have big ambitions for this country and a first minister who, day in and day out, will apply herself to the job of protecting our public services, supporting our businesses and tackling inequality."
Ms Sturgeon told MSPs: "I am ready and willing to take on these responsibilities. There is a job to be done - a big job to be done."
She added: "I look forward now to getting on and doing it."
She described becoming first minister as a "great honour and an immense responsibility".
Ms Sturgeon is also expected shortly to announce the make-up of her cabinet and junior ministerial team.
MSPs went through the process of voting for candidates for first minister on Wednesday afternoon.
Scottish Conservative leader Ruth Davidson also put her name forward as a "Unionist alternative", although the SNP's parliamentary majority helped to ensure Ms Sturgeon got the job as Scotland's fifth first minister.
Ms Sturgeon received 66 votes, the Scottish Conservative leader got 15 and there were 39 abstentions.
On Thursday, Ms Sturgeon will be formally sworn into the role before Scotland's judges in the Court of Session in Edinburgh, and will receive a Royal Warrant.
She is also expected to appoint a deputy first minister, possibly as part of a wider reshuffle of the Scottish government's ministerial team later in the week.
Mr Salmond, who stood down as first minister and SNP leader in the wake of the "No" vote in September's Scottish independence referendum, is staying on as the MSP for Abderdeenshire East.
However, the former MP is also considering standing for Westminster in the 2015 UK election.
Ms Sturgeon's friends and family were present at Holyrood to see her become first minister.
The politician's mother, Joan Sturgeon, said her daughter had achieved her life's ambition and she was "very, very proud" of her.