Virginia’s new governor has already startled this genteel, tradition-bound Southern capital, and not in the way you’d expect of a man who has wrestled an alligator, chummed around with Bill Clinton and orchestrated deal after controversial deal.

In the nine weeks since Election Day, political observers say, Terry McAuliffe (D) has been shockingly gubernatorial.

With moderate Cabinet picks and an ardent courtship of Republicans, the colorful former Democratic National Committee chairman and political fundraiser has projected an image of seriousness, caution and bipartisanship that critics had doubted he could muster.

His deliberate approach appears meant to win over skeptics in both parties who dismissed him as a flamboyant Washington insider with no interest or experience in state politics before his failed bid for governor four years ago. He especially needs to woo Republicans if he wants to get his priorities through a House dominated by the GOP and a Senate where control is in flux.

“I was expecting it was going to be crazy liberals and political hacks,” Del. David B. Albo (R-Fairfax) said of McAuliffe’s Cabinet appointees. “And I have been very surprised — pleasantly surprised — that he really seems to be appointing people who know what they are doing, who are mainstream, who know how to run a government, who’ve been in the job before. So, pretty impressed.”

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The strategy offers a window on McAuliffe’s ambitions as governor, a position that his Republican rival had suggested the Democrat wanted merely as a feather in his cap. (“Some people run to do something, and some people run to be something,” then-Attorney General Ken Cuccinelli II often said.) McAuliffe’s cannily considered start suggests that he wants not only to be governor but also to be a successful one.

Whether McAuliffe, who was sworn in Saturday, can resist his swashbucklingly partisan instincts for four years is an open question. But his surprisingly pragmatic start has at least some conservatives warming to him, even as they remain staunchly opposed to his marquee legislative goal: expanding Medicaid under the federal health-care law.

McAuliffe has surrounded himself with appointees with long track records in state government. Among them are holdovers from the administration of his Republican predecessor, former governor Robert F. McDonnell, including Health and Human Services Secretary Bill Hazel and Finance Secretary Richard D. Brown, who started in state government in 1971.

“People thought they were going to get Michael Moore and Bernie Sanders,” said Del. Mark D. Sickles (D-Fairfax), referring to the liberal filmmaker and the socialist U.S. senator from Vermont. “And instead they got Ric Brown and Bill Hazel.”

“To run a $35 billion-a-year operation from scratch without having the background — and nobody does except Mills Godwin — it’s a steep learning curve,” Sickles added, referring to the only two-term governor in modern Virginia, where the constitution bans back-to-back terms but allows governors to return after a break. “For any incoming governor to keep some experienced hands around is a very wise thing to do.”

Former governor L. Douglas Wilder (D) said he had advised McAuliffe after the election to fill his administration with people who know state government rather than with political friends.

“People are going to be jabbing him for, ‘I want this. I want that. I want the other.’ They’re going to be wanting jobs,” Wilder said. “This is a window of opportunity for him to seize upon structuring — I wouldn’t call it a middle-of-the road administration, but an administration that’s not meant for punishing anyone or favoring anyone but recognizing the need to represent everybody.”

McAuliffe was the picture of the sober chief executive Saturday as he consented to don a formal morning suit for his inauguration and went off to live in a 200-year-old mansion with one of the nation’s last state butlers. As a champion fundraiser for Bill and Hillary Rodham Clinton and as an often-controversial businessman, McAuliffe is better known for pairing a Hawaiian shirt with a bottle of Bacardi on national TV than for sporting a formal cutaway coat with striped trousers.

His freewheeling style did not always play well in the governor’s race, during which McAuliffe had to fend off questions about two ongoing federal investigations into the electric-car company he co-founded. McAuliffe lost a key business group’s backing after he was perceived to have winged it through his endorsement interview. Asked how he would advance his priorities, McAuliffe said that as an Irish Catholic, he was inclined to take legislators out for drinks, three people involved told The Washington Post.

The episode was a low point for his campaign, feeding a narrative that McAuliffe was uninformed and superficial despite all the time he had spent on the trail studiously jotting down notes in spiral pads. It reinforced a gaffe from early in the race, when McAuliffe had to duck in an interview when asked whether he could name the Cabinet positions.

“They misinterpret lack of experience for lack of smarts,” Wilder said. “Terry’s a very smart guy. He’s a very bright guy, very energetic. Critics confuse his effervescence and exuberance with giddiness.”

Since his election, McAuliffe has worked to improve his image with Republicans. He has reached out to every GOP legislator in phone calls and face-to-face meetings, presenting himself as a business-oriented, pragmatic executive. He has cozied up to McDonnell, his predecessor, who remains popular despite a gifts scandal that has him on the verge of indictment. McAuliffe has heaped praise on McDonnell for assisting his transition and even made a public service announcement with the outgoing governor to promote the Republican’s “Holiday Hoops Classic” charity event.

“Usually, if somebody is on the verge of being indicted, they’d be radioactive,” said Bob Holsworth, a longtime Richmond political observer. “The governor-elect is making commercials with him.”

Above all, McAuliffe’s Cabinet picks have done much to assuage concerns about his ability to govern.

“One of my personal concerns was the lack of baseline experience he’s had in governance,” said Senate Majority Leader Thomas K. Norment Jr. (R-James City). “I’m very encouraged that he listened to his advisers on the transition team and retained people who are very experienced.”

Said Del. Christopher Kilian Peace (R-Hanover): “As a person who seems to fly at a 30,000-foot view, it has been a positive development that he has engaged and retained people who can help him manage and run the state.”

McAuliffe’s Cabinet selections, which still need General Assembly approval, have not been universally cheered. Most notably, some abortion-rights activists were upset by Hazel’s reappointment because he had not publicly objected to antiabortion measures imposed under McDonnell.

Ray Allen, a longtime Republican strategist, quibbled with the Cabinet for another reason — its perceived lack of a “wow” factor, saying he had expected McAuliffe to reel in a big name from the business world for secretary of commerce and trade. His pick was Maurice Jones, a former newspaper publisher who most recently served as deputy secretary of the U.S. Department of Housing and Urban Development.

“With all of his contacts all over the world and Washington, and saying, ‘This is the most important thing in my administration,’ I was expecting to pick up the paper one day and say, ‘Wow,’ ” Allen said. “And I get a bureaucrat from Washington?”

Jones has been heartily praised by others, including state Sen. William M. Stanley Jr. (R-Franklin), a classmate from Hampden-Sydney College.

Allen did give McAuliffe credit for making inroads with Republicans in other ways.

“I will give him a hat tip. He talked to every blasted [GOP] member of the General Assembly,” Allen said. “I’m not sure he said much, but that was a smart thing to do. . . . Most of my Republican brothers and sisters are still looking around to see what he’s going to do.”