"I'm very humbled by this," Weiler said. "I pledge to do my very best for you. Now please go home and get your kids to bed."
Randy Shumway was the runner-up, capturing 42.4 percent of the vote.
The vacancy in Senate District 23 happened when Liljenquist announced he was challenging Sen. Orrin Hatch, R-Utah, for the seat he's held since being elected in 1976.
In his time in the Legislature, Liljenquist was known for taking on pension reform and Medicaid reform. He was elected in 2008 after defeating Ron Mortensen a candidate in Thursday's special election who was eliminated in the third round in a primary.
Weiler told the delegates he was best prepared to step into the Legislature in 13 days and "would fight to end earmarks in the state budget."
He also ran on a platform to keep education decisions at the local level.
"It's not the Legislature's job to act like a super school board," he said.
Weiler is a lawyer and former vice chairman of the state Republican Party.