Shares in Vivo, which has a network of about 2,330 service stations across Africa, jumped as much as 21% to 134.8 pence, just below the total offer that equates to about 139 pence.
Vivo shareholders will receive $1.79 in cash for each share they hold, and six cents as an interim plus special dividend.
Netherlands-based Vitol, which is the top Vivo investor with a 36.1% stake, will also buy out Helios, the second biggest shareholder.
Vivo was founded after Shell divested some of its downstream business in 2011. Vitol, Helios and Shell operated Vivo as a joint venture before the two top shareholders bought out Shell for $250 million in 2016.
The board of Vivo plan to unanimously recommend the deal to shareholders, the companies said.
Vitol had engaged with Helios on many occasions in recent years to buy Helios' 27.1% stake. The two agreed on the purchase price of $1.79 per Vivo share, which represents a premium of about 25% to the stock's Wednesday close.
"Since we founded Vivo with Helios and Shell, we have believed in the business' potential and we are excited to have it within the Vitol family, as a pillar of our strategy in Africa," Vitol Head of Origination Chris Bake said.
Founded in Rotterdam in 1966, Vitol has about 6,600 retail sites on four continents, its website showed.
Vitol's offer on Thursday follows a lower proposal in February, which was rejected by the company's board.
Vivo's long-standing Chief Executive Christian Chammas earlier this month said he would retire in 2022. The company has performed well amid the pandemic, with shares having risen more than 50% so far this year.
(Reporting by Yadarisa Shabong and Pushkala Aripaka in Bengaluru; Editing by Uttaresh.V and Shailesh Kuber, Elaine Hardcastle)
By Yadarisa Shabong