The penalties include a record £497m payment to Britain's Serious Fraud Office (SFO) and if finalised would see a prosecution of the company suspended.
It is the largest penalty ever levied by the SFO and is understood to be the largest enforcement action relating to any criminal allegations in the UK.
Rolls-Royce, which makes engines for military jets, ships and submarines, has reached similar agreements with the US Department of Justice and Brazil's Ministerio Publico Federal.
The company said: "These agreements relate to bribery and corruption involving intermediaries in a number of overseas markets, concerns about which the company passed on to the SFO from 2012 onwards.
"These are voluntary agreements which result in the suspension of a prosecution provided that the company fulfils certain requirements, including the payment of a financial penalty."
Rolls-Royce said it had cooperated fully with authorities and would continue to do so.
The SFO confirmed that a deferred prosecution agreement had been reached with Rolls-Royce, subject to a court hearing on Tuesday.
Rolls-Royce will pay interest on the £497m penalty, plus legal costs.
It is paying $170m in US fines and $26m in Brazil, with payments totalling £671m at current exchange rates.
The company said in 2012 that it had passed information to the SFO relating to concerns about bribery and corruption, following a request from the body about allegations of malpractice in Indonesia and China.
It said then that its investigations had "identified matters of concern in these, and in other overseas markets".
The Derby-based group employs more than 50,000 people in more than 46 countries, including more than 24,000 in the UK.
Penalties to the SFO by the company will be paid over five years, with the first year of all three agreements seeing £293m paid out.
Rolls-Royce will publish full-year results next month and said that "an appropriate update on the implications of these agreements" would be given at that time.