Mia Mottley said in a written address that it was “time to fully leave our colonial past behind”.
She quoted the Caribbean island nation's first premier, Errol Barrow, who warned against "loitering on colonial premises".
Reading Ms Mottley’s speech, the governor-general of Barbados, Dame Sandra Mason, said: "The time has come to fully leave our colonial past behind. Barbadians want a Barbadian head of state.
"This is the ultimate statement of confidence in who we are and what we are capable of achieving.
"Hence, Barbados will take the next logical step toward full sovereignty and become a republic by the time we celebrate our 55th anniversary of independence."
The country gained its independence from Britain in 1966, but the Queen remains its constitutional monarch.
The move to declare Barbados a republic has been a long time coming: in 1998, a Barbadian constitutional review commission recommended republican status; and, in 2015, the then prime minister, Freundel Stuart, said: "We have to move from a monarchical system to a republican form of government in the very near future."
Most Caribbean countries have kept formal links with the British monarchy after achieving independence, but Barbados will join Trinidad and Tobago, Dominica and Guyana in cutting ties if it proceeds with its plan.
Jamaica has also indicated that it plans such a transition, with its prime minister, Andrew Holness, saying it is a priority of his government.
Barbados took another step towards independence from the UK in 2003 when it replaced the London-based Judicial Committee of the Privy Council with the Caribbean Court of Justice, located in Trinidad and Tobago's Port of Spain, as its final appeals court.
Additional reporting by agencies
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