Unofficial results gave the 41-year-old Jolly 45 percent of the vote. State Rep. Kathleen Peters finished second with 31 percent and Mark Bircher was third with 24 percent, the Tampa Bay Times reported.
Jolly will square off against Democrat Alex Sink and Libertarian Lucas Overby in a March 11 special general election.
Young, who died Oct. 18, had announced he would not seek re-election this year. He had served in the House since 1971, making him the longest-serving GOP member of Congress at the time of his death.