The Exxon CEO potentially faces a tough fight to be confirmed in the Republican-controlled Senate. Some lawmakers worry about his links to Moscow and opposition to U.S. sanctions on Russia, which awarded him a friendship medal in 2013.
But several Republican establishment figures, including former secretaries of state James Baker and Condoleezza Rice, and former Defense Secretary Robert Gates vouched for Tillerson, 64, who has spent more than 40 years at the oil company.
Rice and Gates, who have worked for Exxon as consultants, both issued statements of support on Tuesday.
Their backing could be crucial for Tillerson getting approved by the Senate, where Republicans will have a slim majority when Trump takes office on Jan 20.
“The fact that Condi Rice, James Baker and Bob Gates are recommending Tillerson carries considerable weight,” said Senator Jeff Flake, a member of the Senate Foreign Relations Committee.
By choosing Tillerson, Trump adds another person to his Cabinet and circle of advisers who may favor a soft line toward Moscow, which is under U.S. sanctions for its 2014 annexation of Crimea and at the center of allegations that it launched cyber attacks to disrupt the U.S. presidential election.
Republican foreign policy hawks in the Senate like John McCain and Lindsey Graham are likely to give Tillerson a rough time at a confirmation hearing in early January.
"It's very well known that he has a very close relationship with (Russian President) Vladimir Putin," said McCain, the Republican party's 2008 nominee for president.
Republicans will have a majority of just 52-48 in the Senate, and only a few defections from their ranks would block Tillerson if every Democrat also opposed him.
Trump said in a statement that Tillerson will reverse policies that left America less safe. "He will be a forceful and clear-eyed advocate for America's vital national interests," Trump said.
Tillerson has foreign experience from years of cutting deals with foreign countries for his company, the world's largest energy firm, but like Trump he has never held public office.
He has been chief executive of Exxon Mobil since 2006. He said in a statement that he shared the president-elect's "vision for restoring the credibility of the United States."
Exxon Mobil's board will meet soon regarding its transition, CNBC reported citing a company statement.
Trump was also poised to add another figure with close ties to the oil industry to his Cabinet.
A source close to the transition said Trump had chosen former Texas Governor Rick Perry, whose state is a leading oil producer, as his nominee for energy secretary, with an announcement expected soon.
Perry met Trump at Trump Tower in New York on Monday, part of a series of meetings that included Rapper Kanye West on Tuesday.
In 2013, Putin bestowed a Russian state honor, the Order of Friendship, on Tillerson, citing his work "strengthening cooperation in the energy sector."
There also has been controversy over alleged Russian interference in the Nov. 8 presidential election, with the CIA concluding that Moscow had intervened to help Trump defeat Democrat Hillary Clinton.
Tillerson's "cozy ties to Vladimir Putin and Russia would represent an untenable conflict at the State Department," Representative Eliot Engel, the ranking Democrat on the House of Representatives Committee on Foreign Affairs, said in a statement.
Trump is confident Tillerson can get past questions about his ties to Russia, a transition official said.
"His relationships with leaders all over the world are second to none," Trump said.
Russian Foreign Minister Sergei Lavrov said Trump and Tillerson were "pragmatic people" who could help America and Russia build a mutually beneficial relationship.
There also are concerns among lawmakers about former U.N. Ambassador John Bolton, who has been mentioned as a possible No. 2 in the State Department and who has voiced hawkish views on Iraq and Iran, as well as on China and Taiwan.
Republicans and Democrats said they would ask Tillerson, who has met Putin several times, about his contacts with Russia. A Kremlin foreign policy aide said Tillerson has good relations with Putin and many other Russian officials.
The U.S. business community welcomed Trump's choice of Tillerson, with GE Chairman and CEO Jeffrey Immelt calling him "a great negotiator."
"We are pleased that Rex will bring a business perspective to the State Department," the National Association of Manufacturers added.
Global Witness, an international group that focuses on natural-resource related conflict and corruption, urged the Senate to reject Tillerson, citing Exxon deals with governments in Nigeria and other countries, which the group said contributed to corruption.
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