Portia Simpson Miller’s pledge came as she took the oath of office and said her administration would adopt a republican form of government.
As she was sworn in for the second time, she also pledged to ease its deep poverty, boost the faltering economy and heal political divisions.
Ms Simpson Miller took the oath of office before roughly 10,000 guests on the grounds of the rambling, colonial-style mansion that is the official residence of the governor-general.
The 66-year-old politician scored a dramatic victory in last week’s national elections, leading her slightly left-leaning People’s National Party to a 2-to-1 margin in parliament over the centre-right Jamaica Labour Party. Her party won 42 seats in the 63-seat parliament.
Making her inaugural address, the Prime Minister said: “I love the Queen. She is a beautiful lady, and apart from being a beautiful lady, a wise lady and a wonderful lady,” she then added in Jamaican patois: “But I think time come.”
Jamaica celebrates its golden jubilee this year, having declared independence in 1962, but it has remained within the Commonwealth.
Ms Simpson Miller added: “This 50th anniversary year will be a time for reflection on the lessons of the past; and as we celebrate our achievements as an independent nation, we now need to complete the circle of independence.”
She added: “In this regard, we will therefore initiate the process of our detachment from the monarch to become a republic with our own indigenous president as head of state.”
A Buckingham Palace spokesman said: “The issue of the Jamaican head of state is entirely a matter for the Jamaican government and people.”
The plainspoken, charismatic Ms Simpson Miller, the island’s first female prime minister, takes over from Andrew Holness.
“After being tested and tempered, I stand before you today a stronger and better person prepared to be of service to my country and people,” Ms Simpson Miller said at the start of her 45-minute speech.
She also said she will replace the Privy Council in London with the Trinidad-based Caribbean Court of Justice as Jamaica’s highest court of appeal. She said this will “end judicial surveillance from London.”
She vowed her government will “ease the burdens and the pressures of increasing poverty, joblessness and deteriorating standards of living” while also pursuing a tight fiscal policy and forging strong partnerships with the private sector and international partners such as the International Monetary Fund.
“My administration will work tirelessly that while we try to balance the books we balance people’s lives as well,” Ms Simpson Miller said.
The prime minister also urged Jamaicans to create a more civil and respectful society and earnestly strive to make the best of themselves.
Ms Simpson Miller is not the first Jamaican leader to promise to move towards a republic.
In the early 1990s, then-Prime Minister PJ Patterson also said it was time for the island to have its own head of state.