Thousands turned out for her inauguration including the Caribbean's top leaders as well as the Nation of Islam's Louis Farrakhan and Essence magazine editorial director Susan Taylor.
"The first pledge I make as prime minister is to advance human rights and individual liberties," the 60-year-old leader said. "I pledge to work tirelessly to end all corruption and extortion. Both of these diminish our economic potential and I will do everything in my power to break the power of the criminals."
Simpson Miller, known as "Sista P," was a long-serving member of parliament who represented South East St. Andrew Parish, one of Jamaica's crime-ridden slums that she says can be transformed with better schools and more economic opportunity.
She said her ascension to Jamaica's leadership post was "a true manifestation of the Jamaican dream. This indicates that any child regardless of circumstances can rise to the top."
Patterson's administration was dogged by scandals and allegations of corruption while the economy lagged and the crime rate soared — a record 1,671 homicides occurred last year in the nation of 2.6 million.
Simpson Miller's supporters say they hope that her becoming the first female prime minister will inspire others in a country where about 12 percent of political posts are held by women.