The vessels are 95 feet long and can travel at a speed of more than 25 knots. They will be armed with a 30mm cannon and two 25mm guns. A helicopter flight deck is included in the design.
BAE said the vessels were built for the government of Trinidad and Tobago under a 2007 contract, which was later canceled.
The value of the sale to Brazil is $172 million.
The contract with Brazil includes a manufacturing license agreement, under which Brazil will be able to construct additional ocean patrol boats.
"This is a significant step forward in our relationship with Brazil," said Andrew Davies, managing director of BAE Systems' Maritime business. "The ocean patrol vessels are highly capable ships and I am sure they will be a tremendous asset to the Brazilian navy.
"We are looking forward to working together and hope this will be the start of a long- term partnership with Brazil in the maritime sector."