GOP voters also picked state Sen. Ralph Hudgens as their nominee for the open insurance commissioner seat and conservative activist Tim Echols for a spot on the Public Service Commission.
Democrats, meanwhile, chose state Rep. Georganna Sinkfield to challenge Republican Secretary of State Brian Kemp in November for a term as the state's top election official.
In what was the most high-profile of the down-ticket statewide races, unofficial returns showed Olens leading state Sen. Preston Smith with 59 percent of the vote after 95 percent of the precincts reported.
Throughout the runoff race, Smith sought to play up his Georgia roots and tried to cast Olens as a carpetbagger from New Jersey with liberal leanings. But Olens countered by emphasizing his role as a fiscal conservative and questioned Smith for missing crucial votes during the legislative session.
The two were forced into a runoff when neither emerged from the three-person primary with more than 50 percent of the vote. The winner will face Democrat Ken Hodges, a former Dougherty County prosecutor, in the race to succeed Attorney General Thurbert Baker, who waged an unsuccessful bid for governor instead of seeking re-election.
Olens said he has already shifted his focus to the November election, and that he plans to campaign heavily in south Georgia where Hodges attracted a chunk of his primary support.
"A lot of folks thought as the former chair of Cobb County I was going to campaign solely in the region, but I've been everywhere - and it's paid off. We're going to continue to do that," he said. "I'm going to work the entire state."
In the campaign for secretary of state, Sinkfield defeated Sen. Gail Buckner with 59 percent of the vote. Sinkfield will face Kemp, a former state senator from Athens who was appointed to the office in January after Karen Handel resigned to run for governor.
Hudgens edged out attorney Maria Sheffield, attracting about 55 percent of the vote. The two emerged from a crowded, nine-person GOP primary in the campaign to succeed John Oxendine, who also decided to run for governor.
Both Republicans vowed to oppose Obama's sweeping health care plan, but Hudgens emphasized his experience as the chair of the Senate Insurance Committee. He also vowed to build on Oxendine's decision earlier this year to refuse to set up a state insurance pool for high-risk Georgians as part of the overhaul.
Hudgens will face Democrat Mary Squires, who ran unopposed in her party's primary.
The race for an open seat on the Public Service Commission has attracted little attention, but the complicated issues that come before the five-member board are worth billions of dollars to utilities and directly affect the everyday lives of Georgia residents.
Echols, who earned 52 percent of the vote to defeat state Sen. John Douglas, will face Democrat Keith Moffett in November. The winner takes the seat held by the retiring Bobby Baker, widely known as the panel's most vocal consumer advocate.
Echols, for one, vowed to follow Baker's lead and be an outspoken advocate for alternative energy.
"I intend to follow in his footsteps. I respect him immensely and I hope I can be the conservative watchdog on this commission," he said. "I know I'm going to ask the tough questions and scrutinize and negotiate on behalf of consumers."