MEXICO CITY—President Enrique Peña Nieto is set to unveil a long-awaited proposal to change the constitution to try to lure back major private oil companies to Mexican oil fields for the first time since the country's 1938 nationalization, a move that could attract billions of dollars in investment and boost Mexico's image as an emerging economy.

The stakes are high for the new president, who took power last December for a six-year term. The proposal, expected to be delivered to the Senate on Wednesday, is seen as a make-or-break...