Condoleezza Rice, Robert Gates, Stephen Hadley and James Baker, all of whom have business dealings with the oil giant, played a crucial role in convincing Trump's team to select Tillerson to become America's top diplomat.
A source familiar with discussions over the nomination said that Vice President-elect Mike Pence reached out to Rice and Stephen Hadley, who served as George W. Bush's national security adviser, a few weeks ago asking for good candidates for secretary of state and other positions.
Rice, Hadley and Gates "could see they were struggling with who the secretary of state ought to be," the source told CNN.
After discussing possible candidates, a consensus emerged that Trump needed someone with a "different profile," the source said, adding that, "going to the establishment didn't feel right for this particular president."
Rice and Hadley worked with Tillerson in his capacity as CEO of ExxonMobil and felt that his global business experience was wide-ranging enough to qualify him for the job. They also vouched for his grasp of global geopolitics.
"Oil is about geopolitics with a capital 'G,'" the source said, noting that Tillerson's knowledge extends well beyond Russia and into the Middle East and Indonesia. "You do business in the toughest places with the toughest characters and Rex is the best of that group."
That Tillerson has dealt with leaders like Putin in a professional business setting and understands the upsides and downsides of negotiations also appealed to Trump, the source said.
Tillerson was already an out-of-the-box choice to run the State Department, having come from the private sector and nominated to a position which traditionally has gone to established government officials or politicians.
Rice and Gates, two top Cabinet officials in the George W. Bush administration, released statements on Tuesday celebrating the selection of Tillerson.
"Rex Tillerson is an excellent choice for secretary of state. He will bring to the post remarkable and broad international experience; a deep understanding of the global economy; and a belief in America's special role in the world," Rice said. "I know Rex as a successful businessman and a patriot. He will represent the interests and the values of the United States with resolve and commitment. And he will lead the exceptional men and women of the State Department with respect and dedication."
Neither Gates nor Rice specifically addressed his ties to Russia, which are expected to be a flashpoint in his confirmation hearings.
"I strongly endorse the President-elect's selection of Rex Tillerson to be the next secretary of state. He would bring to the position vast knowledge, experience and success in dealing with dozens of governments and leaders in every corner of the world," Gates said. "He is a person of great integrity whose only goal in office would be to protect and advance the interests of the United States."
Gates and Rice were both quite critical of Trump during the election, with Gates at one point saying Trump was "beyond repair" and "unfit to be commander-in-chief." Rice called for Trump to leave the presidential race in October, as he became mired in sexual assault allegations.
Other Bush officials praised the choice of Tillerson, including former Vice President Dick Cheney
and Baker, who worked both for George W. Bush and his father's administration.
"Rex Tillerson, who is a friend of mine, is an excellent choice to head the State Department and has an opportunity to be a very effective secretary of state," Baker said. "As CEO of one of the world's largest and best-run companies, has demonstrated the management and negotiating skills, and has the international experience, that are required in the job."
Baker's firm, Baker Botts, also has aextensive ExxonMobil ties: the firm has represented Exxon on cases involving allegations of natural-gas price fixing
and issues related to gas pipeline rates. And the firm has also represented Russian state-owned oil company Rosneft on a deal with Exxon
and other companies related to "difficult-to-extract resources of hydrocarbons in Russia," according to a Baker Botts news release.