Former Exxon Mobil chief overcame concerns about close ties with Russia’s Putin.

The Senate on Wednesday confirmed former Exxon Mobil Corp. CEO Rex Tillerson as secretary of state, sending him to the State Department as career officials mount a formal protest against President Donald Trump’s immigration initiative and the U.S. faces a complex set of foreign-policy challenges. Mr. Tillerson won over skeptical Republicans, including Sens. John McCain of Arizona and Marco Rubio of Florida, but continued to face Democratic opposition. He was confirmed on a 56-43 vote. Senators had voiced concern about the close relationship Mr. Tillerson forged with Russian President Vladimir Putin while he was at Exxon and his unwillingness in testimony to recommit the U.S. to Russia sanctions. Democrats also were critical of his views on climate change.

Mr. Tillerson’s confirmation was the most contentious for secretary of state in at least 50 years, coming with the support of only three Democrats—Sens. Heidi Heitkamp (D., N.D.), Joe Manchin (D., W.Va.), Mark Warner (D., Va.)—and Angus King, a Maine independent who caucuses with the Democrats.

Now, the former business executive, 64 years old, will have to move quickly to get senior staff in place, calm hundreds of officials who have registered concerns about Mr. Trump’s immigration and refugee policies, and carve out a place for himself in the Trump administration’s foreign-policy apparatus, which so far has been dominated by White House aides Steve Bannon and Jared Kushner.

The immediate challenges Mr. Tillerson will confrontwhen he enters office, according to current and former U.S. officials working on foreign policy, include addressing the rift with Mexico over Mr. Trump’s plans to build a border wall; implementing and dealing with a temporary immigration ban on seven Muslim-majority countries intended to protect against terrorism; and possibly implementing Mr. Trump’s suggestion to relocate the U.S. embassy in Israel to Jerusalem from Tel Aviv.

In the longer term, Mr. Tillerson will be asked to make good on Mr. Trump’s pledge to recast U.S. relations with major global powers Russia and China, to help intensify the war against the terrorist organization Islamic State, and revisit the nuclear agreement that the Obama administration forged with Iran in 2015. Mr. Tillerson was sworn in by Vice President Mike Pence at a White House ceremony Wednesday evening and was expected to go to the State Department on Thursday. He will go straight to work, meeting Thursday with Jordan’s King Abdullah II and German Vice Chancellor Sigmar Gabriel. Mr. Tillerson has begun the process of setting up his own State Department team. He is expected to name Margaret Peterlin, a former Navy officer and senior official at the Patent and Trademark Office during the Bush administration, as his chief of staff, according to people familiar with the deliberations.

Paula Dobriansky, a former senior State Department official in the George W. Bush administration, and Elliott Abrams, a former National Security Council aide to Mr. Bush, are among candidates to be deputy secretary of state. Michael Dougherty, who has worked at Raytheon Co. and at the Department of Homeland Security, is expected to be nominated to take the helm of the Consular Affairs Bureau. Rob Wasinger, a former Republican Virginia congressional candidate in 2014, is expected to take on a senior role, the people familiar with the deliberations said. Jennifer Hazelton, who led Mr. Trump’s campaign communications in Georgia and had previously worked at CNN and Fox before moving to politics, is expected to be Mr. Tillerson’s press secretary. The staffing decisions aren’t yet final and could change.

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