Bigelow said his first priority will be to sit down with City Manager Wayne Pyle and police Chief Lee Russo "and just be brought up to speed on the things they're doing and what I can do to support their efforts."
He also wants to review city projects and inform the public of their status.
The job of mayor is officially part-time but "I will devote at least full time to it at the start," Bigelow said.
"I want to make sure the transition to a new mayor goes smoothly," he said.
Lang, who was elected to the West Valley City Council two years ago, said her priority will be serving the remainder of her four-year term.
"We'll see what the future will bring," Lang said, adding that she believes she and Bigelow will work well together on the council.
Bigelow, who will begin a four-year term in January as mayor of the state's second-largest city, will lead a city that has been racked by controversy.
The current mayor, Mike Winder, acknowledged two years ago that he had written positive stories about West Valley under a pseudonym. He announced last spring that he would not run for a second term, citing the need for a full-time job so he can support his family.
More recently, the West Valley City Police Department has been the center of controversy revolving around allegations of mishandled evidence in scores of narcotics cases and last year's fatal shooting by two detectives of 21-year-old Danielle Willard during an alleged drug bust.
Bigelow, 64, is a certified public accountant who represented West Valley City in the Utah House from 1995 until he gave up the seat in late 2010 to become state budget director. He retired from that position in January. Before that, Bigelow was a finance manager with The Church of Jesus Christ of Latter-day Saints for 28 years.
Lang, 54, is in her first term as a City Council member after serving on the Planning Commission for a decade and the city's tree committee for 15 years. She and her husband have owned and operated Oakbridge Greenhouse in West Valley City for 30 years. Lang, if elected, would have become the city's first female mayor.
They were the top two vote-getters among seven candidates in an August primary Bigelow earned 37 percent of the vote, Lang 17 percent.
Voters in West Valley also were choosing three city council members.
In unofficial results, math teacher Lars Nordfelt defeated Phil Conder, a budget and administrative officer, for an at-large seat. The position is now held by Don Christensen, who ran for mayor and was defeated in the primary.
In District 2, incumbent Steve Buhler won a second term, defeating challenger Jeff White. Buhler is an attorney and White is a research and development systems specialist.