The two OPEC oil producers also signed a preliminary agreement, showing the political will to strengthen relations although the economic impact remains unclear.
In Riyadh, Tinubu said he wanted to "assure all potential Saudi investors of the safety of their investments" in Nigeria, according to his office.
Tinubu came to power in May and quickly introduced economic reforms aimed at restoring public finances and attracting more foreign investment.
His administration has ended a fuel subsidy and floated the naira currency -- but in the short-term, Nigerians are struggling with a tripling of fuel prices and higher food costs.
Foreign direct investment into Nigeria's economy dropped from $2.2 billion in 2014 to $470 million in 2022, according to the Institute for Security Studies think tank.
On the eve of the summit, Nigeria's oil minister Heineken Lokpobiri announced he had signed a memorandum of understanding with his Saudi counterpart Prince Abdulaziz bin Salman on "strengthening our partnership in the oil and gas sector."
"We can anticipate enhanced technological exchange, investment inflow and a strengthened strategic partnership," he said on social media.
Saudi Arabia's relations with African countries, especially those with large Muslim populations, began to grow in the 1970s.
Nigeria, Africa's leading oil producer, and Saudi Arabia are both members of the Organisation of the Petroleum Exporting Countries (OPEC) and the Organisation of Islamic Cooperation (OIC).
While Saudi Arabia's diplomatic presence in Africa has risen considerably in recent years, its economic involvement remains limited, despite the creation a year ago of a Nigeria-Saudi Chamber of Commerce.
"Energy cooperation between the two countries only exists through discussions at summits and meetings of OPEC... But no significant investment by Saudi Arabia in the Nigerian oil sector has materialised," said Benjamin Auge, a researcher at the French Institute of International Relations (IFRI).
He said the energy agreement signed between Abuja and Riyadh "will probably remain more in the realm of good intentions."