The ExxonMobil chairman and chief executive was described as "a world-class player" by the US President-elect when he spoke to Fox News on Sunday.
Mr Trump added: "To me, a great advantage is he knows many of the players and he knows them well.
"He does massive deals in Russia, he does massive deals not for himself (but) for the company."
In a tweet announcing his choice, Mr Trump described Mr Tillerson as "one of the truly great business leaders of the world".
Mr Tillerson, 64, has held the top jobs at ExxonMobil since 2006 and had been due to retire in March under the company's policy, which sees employees retire at 65.
But the Texan is likely to face a tough confirmation process before the Senate, with issues set to include his close relationship with Russian President Vladimir Putin and his views on climate change.
And while he may have experience in making business deals with other nations, he has no experience working with them as a diplomat.
He was trained as an engineer and has never worked in government.
He first met Mr Putin in the 1990s while supervising an Exxon project on Sakhalin Island and they became closer after Mr Putin took over from Boris Yeltsin in December 1999.
In 2011, a deal was signed between Exxon and Russia's public energy giant Rosneft to explore and drill in the Arctic and Siberia, a deal that could generate hundreds of billions of pounds.
Two years later, Mr Putin bestowed the Order of Friendship on Mr Tillerson, saying he had earned the Russian state honour for his work "strengthening cooperation in the energy sector".
Mr Tillerson has been a vocal critic of US sanctions against Russia, which came after its incursion into Crimea in 2014.
ExxonMobil was forced to scrap some projects, and freeze the Rosneft deal, as a result of the sanctions and it suffered at least £800m in losses.
During a shareholders' meeting in 2014, Mr Tillerson said: "We always encourage the people who are making those decisions to consider the very broad collateral damage of who are they really harming with sanctions."
Another issue likely to come up during the oil boss's confirmation battle is climate change.
Mr Tillerson has previously acknowledged that the earth's climate is changing, the average temperature is rising and greenhouse gases are increasing.
But he has also said that climate remains a complex area of scientific study and, despite an increase in energy production from fracking in the US, he has resisted cutting investment in the search for new oil wells.
In 2011, he warned that, should the US step back, a "large consuming country" such as China could "step into that void".
ExxonMobil's scientists recognised climate change as early as the 1970s, according to recently-leaked internal documents, but the company remains under fire for its efforts to undercut climate experts' warnings.
Mr Tillerson's views on foreign policy are little known, apart from his support for free trade and American engagement in the Middle East.
After the Iraq War, ExxonMobil agreed to develop a large project in southern Iraq on terms less favourable to the company than most of its other deals.
Mr Tillerson was paid $27.3m (£21.5m) last year and has accumulated approximately $160m (£126m) in Exxon stock and $149m (£117m) in uninvested stock options, according to a statement filed by the company with the Securities and Exchange Commission.
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