"I congratulate... Yasir al-Rumayyan, governor of the Public Investment Fund, on his appointment as chairman of the board of directors of Saudi Aramco, which is an important step to prepare the company for the public offering," Falih said on Twitter.
Rumayyan, already an Aramco board member, is the head of the vast Saudi sovereign wealth fund that is spearheading an ambitious plan to diversify the kingdom's oil-reliant economy.
The news comes after Falih, who has long headed both Aramco and the energy ministry, has seen his portfolio shrink as the kingdom reels from low oil prices.
Saudi Arabia on Friday announced the creation of a new ministry of industry and mineral resources, separating it from the energy ministry as it steps up efforts to boost non-oil revenue.
"All this shows that in Saudi Arabia there has been some dissatisfaction at the highest levels on how things have been going," Olivier Jakob, from the consultancy Petromatrix, told Bloomberg News.
"Falih has not really fully delivered on oil prices. There's speculation that prices and the IPO are linked and they need higher prices to get the valuation they want for the IPO."
Aramco has said it plans to float around five percent of the state-owned company in 2020 or 2021, in what could potentially be the world's biggest stock sale.
It aims to raise up to $100 billion based on a $2 trillion valuation of the company, but amid low oil prices investors have debated whether Aramco is really worth that much.
Failure to reach a $2 trillion valuation as desired by Saudi rulers is widely considered the reason the IPO, earlier scheduled for 2018, has been delayed.
Earlier this month, Aramco said its first half net income for 2019 slipped nearly 12 percent to $46.9 billion on lower crude prices.
It was the first time the company has published half-year financial results, and comes after Aramco opened its secretive accounts for the first time in April, revealing itself to be the world's most profitable company.
The planned IPO forms the cornerstone of a reform programme envisaged by Crown Prince Mohammed bin Salman to wean the Saudi economy off its reliance on oil.
Saudi Aramco has not announced where the listing will be held, but London, New York and Hong Kong have all vied for a slice of the much-touted IPO.
The oil giant is considering a two-stage IPO, with a domestic debut and a subsequent international listing possibly in Tokyo, the Wall Street Journal reported last week.