She has said Jamaica should stop worrying about her gender and concentrate on the island's problems, particularly the high crime rate.
Ms Simpson Miller was elected president of the governing People's National Party in an internal vote.
The former local government minister narrowly beat the national security minister and two other candidates to the job.
'Firebrand'
Ms Simpson Miller has been a popular figure in Jamaican politics since the 1970s, starting in one of Jamaica's toughest constituencies, often called garrisons.
"She was not Mary Magdelan. She gave as good as she got. You did cross her on the streets of Kingston at that time," Jamaican radio presenter, Cliff Hughes, told the BBC.
"She is seen as someone who has really risen through the ranks of the party, coming from a very, very poor section of Jamaica... to the top post," Radio Jamaica's Kathy Barrett told the BBC.
"She's a woman who's very determined, a firebrand type of politician who has really hit home when it comes to the majority of people - especially women, the poor and the unemployed."
Her predecessor led his party to three election victories and was Jamaica's longest-serving prime minister, but leaves a government dogged by charges of corruption.
Ms Simpson Miller will also inherit a crisis in crime, with the murder rate at a record level, high unemployment, and a struggling education system.
She has faced criticism from the opposition, which says she has proposed nothing new, and from some within her own party.
Foreign Affairs Minister KD Knight has questioned her leadership ability. He announced his resignation on Monday.
The next parliamentary elections are due to take place in 2007.
