U.S. Sen. Kay Bailey Hutchison, Perry's main rival in the GOP race, conceded the election late Tuesday.
"I ask my supporters tonight all through Texas to join me and unite behind Gov. Perry," Hutchison said in Dallas.
By winning Tuesday's primary, Perry -- who held a sizable lead in pre-election polls over Hutchison and newcomer Debra Medina -- avoided an April 13 runoff, the Houston Chronicle reported.
White had been favored in the seven-person race to win the party's nomination for governor in the Nov. 2 general election. His nearest competitor was Houston hair-care magnate Farouk Shami.
White -- a three-term mayor of Houston -- told a crowd gathered in Houston he expects a tough campaign as Perry seeks re-election in November, the Chronicle said.
"Texans deserve a new governor," he said -- a leader who is "more interested in the jobs of Texans than in preserving his own job."
Texans also voted Tuesday in congressional elections, a slew of statewide offices, three state Supreme Court justices, three Court of Criminal Appeals members, 16 state senators, all 150 state representatives, eight members of the state Board of Education, several Court of Appeals justices, district judges, family district judges, county-level judges and many county-level races, the Chronicle reported.
The Justice Department said in a statement Monday it will monitor balloting in Fort Bend, Galveston, Gonzales, Williamson and Wilson counties to ensure compliance with the minority language requirements of the Voting Rights Act of 1965 and other federal voting rights statutes.