The vote over a third candidate proposed by Engine No. 1 was too close to call as of 3 p.m. on Wall Street.
"We're looking forward to welcoming the new directors," Exxon CEO Darren Woods said Wednesday on CNBC's "Closing Bell." "I look forward to helping them understand our plans and then hear their insights and perspectives."
Engine No. 1, which has a 0.02% stake in Exxon, has been targeting the company since December, pushing the it to reconsider its role in a zero-carbon world.
Wednesday's vote came during Exxon's annual shareholder meeting, where Woods fielded questions from shareholders ranging from the company's dividend to its investments in carbon capture technology.