The University of Virginia Board of Visitors unanimously elected Richmond businessman William H. Goodwin Jr. as its vice rector Monday evening, putting him on course to lead the board starting in 2015.

The process of voting Goodwin into the position lasted less than 10 seconds, but it followed weeks of behind-the-scenes campaigning and jockeying for the powerful position on the board that oversees Virginia’s flagship public school.

Gov. Robert F. McDonnell (R) appointed Goodwin as a nonvoting “senior adviser” to the board last summer to provide “wise counsel on an array of matters and to assist the university in solving strategic and communications challenges” after the June 2012 ouster and then reinstatement of President Teresa A. Sullivan. In the fall, board member Randal J. Kirk resigned from the board, and McDonnell appointed Goodwin to fill Kirk’s post.

“It is a tremendous honor,” Goodwin said after the whirlwind vote here Monday. Sullivan did not attend.

Since joining the board, Goodwin has been a controversial figure. At a September board meeting, George Cohen, chairman of U-Va.’s Faculty Senate, told the board that faculty still wanted a full explanation of why Sullivan was ousted, saying that “this crisis has not gone away.”

Goodwin responded: “We need to leave the past alone. You’re trying to dig up things. . . . It’s time to move on.”

On at least two occasions, Goodwin has compared serving on a public governing board to being in a marriage. In an interview with The Washington Post this year, Goodwin criticized reporters for asking questions about the inner workings of the public university’s board, likening the media to a “third party” trying to listen to a couple in the privacy of their bedroom.

“My involvement is really going smoothly,” Goodwin said in the interview, referring to his interactions with administrators and fellow board members. “The only deterrent is the Freedom of Information Act.”

If Goodwin becomes rector, he will lead the board when Sullivan’s contract expires in July 2016.

This is Goodwin’s second tour on the board and his second time as vice rector. He was previously on the board from 1996 to 2004. Although was elected vice rector, Goodwin never progressed to rector because his term ended and he was not reappointed.

That previous experience has given Goodwin an authoritative air on the board, and some call him “Mr. Goodwin,” even in an environment where everyone else uses first names.

Goodwin has made efforts to work with U-Va. administrators on tough issues. Earlier this year, as the board kept putting off Sullivan’s request for it to approve increases in faculty salaries over the next few years, Goodwin stepped in and proposed a resolution that ultimately passed.

He is chairman of the board of CCA Industries, a holding company with several hospitality businesses, including the iconic Jefferson Hotel in Richmond. Goodwin earned a bachelor’s degree in mechanical engineering from Virginia Tech in 1962 and an MBA from U-Va. in 1966. He and his wife, Alice T. Goodwin, have donated millions of dollars to the university and its medical center.

The vote came during the first of two days of board meetings in Charlottesville, the last that will be overseen by Rector Helen Dragas, who is credited with leading last summer’s ouster of Sullivan and has weathered months of criticism because of it. Vice Rector George K. Martin, a Richmond attorney, is set to replace her when she moves to a regular appointed seat on the board.

“Bill’s leadership comes from more than just the breadth and depth of his experience and wisdom,” a statement from Dragas said of Goodwin. “His willingness to ask the challenging questions — and his resourcefulness and collaborative nature to bring people together to find the answers — will serve this Board well into the future.”