Tillerson, 64, became president of the Texas-based oil company in 2004 and has a close business relationship with Russian President Vladimir Putin. He has spent his entire career at the company now known as Exxon Mobil.
The sources cautioned that nothing is final until the president-elect officially announces it, likely next week.
The selection of Tillerson comes after Trump and his transition team spent weeks searching for someone to fill the post of the top U.S. diplomat. Former Republican presidential candidate Mitt Romney and former New York City Mayor Rudy Giuliani were reportedly in the running. Giuliani said Friday he had taken his name out of consideration.
Tillerson will be paired with former U.N. Ambassador John Bolton as his deputy secretary of state for day-to-day management of the department, one source added.
As secretary of state, Tillerson would be fourth in line to the presidency.
Other facts about Tillerson:
Additional reporting by CNBC staff.