Barber, a former aide to Gabrielle Giffords, won the right to represent Arizona’s Second Congressional District.
“I’m really proud and honored that I’ve been given another opportunity to serve,” Barber said, The Associated Press reported.
“I never expected to be in Congress. When I won the special election I was thrilled about that and now I have two years to get some work done.”
Giffords retired from politics after deranged gunman Jared Lee Loughner opened fire at one of her public appearances outside a Tucson grocery store on Jan. 8, 2011.
He shot 19 people and killed six. Giffords survived with a brain injury while Barber had leg and facial injuries.
The results of the Nov. 6 ballot against Republican Martha McSally were much closer than June’s special vote.
They traded the lead during election night by a few dozen votes, the AP said.
McSally, a retired Air Force colonel, called to concede today after Barber established a 1,400-vote lead.
“Our charge is clear: to stand up for middle-class families and look out for southern Arizona’s future,” Barber said in a statement, according to The New York Times.
Arizona isn’t the only close race, however, with election officials recounting ballots in Florida’s 18th Congressional District.
Republican Rep. Allen West asked for and received a recount in his race against Democrat Patrick Murphy.
The St. Lucie County Supervisor of Elections ordered a recount from ballots cast during eight days of early voting, CNN said.
Murphy has a 1,900-vote lead.