Parent company Ferrovial confirmed terms of the deal in a statement over the weekend following long-running negotiations.
Birmingham City Council will receive £160m from the firm this year with the remaining £55m paid over the next six years.
Amey has been locked in a five-year legal battle with the council over performance on its £2.7bn PFI deal. This has already seen Amey Highways suffer serious losses.
The deal will allow Ferrovial to press-ahead with plans to sell its UK support services business Amey.
Ferrovial said: “Amey, a subsidiary of Ferrovial, has reached an agreement with the rest of stakeholders to terminate the Birmingham Highways PFI contract.
“The agreement involves the payment by Amey of £215m, of which £160m will be paid in 2019 and the remaining £55m over the next six years.
“Amey will continue to provide services on an interim basis until 30 September 2019, and this period may be extended until 31 March 2020.
“This agreement does not have impact on the profit and loss account of Ferrovial.”
A joint statement from Birmingham City Council and Amey said:“A consensual settlement agreement has been signed for Amey to exit the Birmingham Highways PFI contract.
“As part of the agreement, Amey will continue to provide services until a replacement contractor is found to deliver those services on an interim basis.
“That interim replacement will be sought as soon as possible, but will be in place no later than 1st April 2020. The full retendering of the project to find a permanent replacement contractor will take place during 2020/21.
“All parties will be working closely in the coming months to ensure the smooth transition of services and staff.”