Aramco will retain a 51% stake in the new company.
EIG, which has invested more than $34 billion in energy and energy infrastructure, was the deal's underwriter and will work with Aramco in the coming days to decide on other parties for the consortium, a source familiar with the deal said.
Abu Dhabi state investor Mubadala is in discussions on being part of it, a spokesman said.
Aramco will retain operational control of the pipeline network and assume all operating and capital expense risk, the companies said. The deal will have no impact on Aramco's oil production.
Aramco will also offer so-called "staple financing" which the buyers can use to back their purchase, sources have told Reuters.
"We will continue to explore opportunities that underpin our strategy of long-term value creation," CEO Amin Nasser said.
Other bidders in the deal process included Apollo Global Management and New York-based Global Infrastructure Partners (GIP).
U.S. asset manager BlackRock and Canada's Brookfield Asset Management Inc stepped away from bidding, Reuters reported on April 6, citing sources familiar with the deal.
Abu Dhabi's National Oil Co (ADNOC) has signed similar deals over the last two years, raising billions of dollars through sale-and-leaseback agreements tied to its oil and gas pipelines.
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