Thompson told the crowd gathered at his victory party that the state's GOP is "on a roll" and that the work of taking back the state begins immediately.
"We have always, in America, ladies and gentlemen, promised our children and our grandchildren that were going to give them a country that is stronger, freer, fairer, safer, with more options than we had," Thompson said. "We've always promised that. And for the first time, ladies and gentlemen, for the first time, I don't think we can fulfill that promise unless we take it back."
Baldwin, a seven-term U.S. House incumbent from Madison who was unopposed in her primary, said Thompson's win gives voters "a clear choice for the November election."
"I will fight to do what's right for the middle class and Thompson will put those at the very top and the big monied special interests in Washington ahead of Wisconsin's hard working families," Baldwin said in a prepared statement after the primary results were announced.
Unofficial results showed Thompson getting more than a third of a vote in the four-way primary, besting his closest rival Eric Hovde 34 percent to 31 percent. Hovde, a first-time candidate, put more than $5 million of his own money into his campaign.
Read more at Wispolitics.com, a media partner of BizTimes Milwaukee