The agreement paves the way for the government to fund and construct a power plant at Tavan Tolgoi.
In February, Rio and Turquoise Hill submitted a feasibility study to the government for a US$924 million power plant.
The parties have agreed to work towards finalising a power purchase agreement by the end of March 2021.
Construction of the plant is due to begin no later than July 1, 2021, with commissioning expected four years later.
Oyu Tolgoi is currently sourcing power from China's Inner Mongolian Western Grid via a back-to-back power purchase agreement with the National Power Transmission Grid and the Inner Mongolian Power Company (IMPC).
The Mongolian government and Oyu Tolgoi have committed to extending the current arrangement to ensure continued stable power is supplied to the mine and underground project until the new plant is commissioned and is able to supply stable, reliable and continuous power.
"This agreement provides a potential pathway to securing a domestic power supply for the Oyu Tolgoi mine and underground project for the benefit of all shareholders and the wider community," Rio Copper & Diamonds chief executive Arnaud Soirat said.
"We look forward to working with the government of Mongolia to progress the solution."
Last month, Turquoise Hill reported updated capital costs and schedule for the troubled Oyu Tolgoi underground expansion.
In July last year, Rio and Turquoise Hill warned of a cost blowout of $1.2-1.9 billion on the $5.3 billion capital costs of the underground expansion after challenging ground conditions required major changes to mine design and a delay of 16-30 months.
Turquoise Hill said it expected a cost increase of $1.5 billion and delay of 25 months, taking likely first production to early 2023.
Rio Tinto owns a 33.5% indirect interest in Oyu Tolgoi through its 50.8% shareholding in Turquoise Hill, which holds 66% of the project in joint venture with the Mongolian government.