The deal adds a further two years to an existing five-year contract with the state oil company.
Said team chief Frank Williams: "There can be no stronger validation of the value of a partnership than to see it extended to seven years in duration.
"We at the BMW WilliamsF1 Team know only too well the value that committed technical partners such as Petrobras can make to our on-track performance.
"I am delighted that the commercial and technical benefits in return prove to be as attractive for our business partners."
