The CEO of electric automaker Tesla Motors tweeted that he thinks Tillerson "has the potential to be an excellent Sec of State."
On Monday, the Senate Foreign Relations Committee narrowly approved Tillerson in an 11-10 vote, allowing him to move forward in the confirmation process. The vote split along party lines, but the former oil executive is expected to be confirmed in the wider Senate vote, where Republicans hold 52 seats.
"Rex is an exceptionally competent executive, understands geopolitics and knows how to win for his team. His team is now the USA," Musk tweeted.
Musk has been outspoken about climate change. In September, Musk tweeted "turns out ExxonMobil not 100% forthcoming about climate change" along with a link to a story.
The Tesla CEO has also tweeted, calling the denial of climate change "real fraud."
"I came to the conclusion a few years ago that the risk of climate change does exist and that the consequences of it could be serious enough that actions should be taken," Tillerson said before the Senate Foreign Relations Committee earlier this month.
But Tillerson did not directly respond to a question as to whether human activity is causing climate change.
— CNBC's Tom DiChristopher contributed to this report.