Wolf, 42, made his announcement Tuesday evening before 300 cheering supporters in Overland Park, the Kansas City Star reported.
A radiologist, Wolf is a well-known figure among conservative Republicans. He writes a conservative-leaning Internet column, has appeared on Fox news programs and has been mentioned on Rush Limbaugh's radio talk show. Ironically, he is also a cousin to President Barack Obama.
He is the latest Tea Party challenger to a sitting GOP senator. In 2012 several right-leaning candidates took on established Republican incumbents in primaries, the newspaper noted.
Roberts, 77, has thus far not drawn a Democratic challenger for his seat. He had nearly $1.5 million in his campaign bank account at the end of June, the Center for Responsive politics reported, as well as the endorsement of leading Kansas Republicans.
"It's hard to imagine Roberts being seriously tested by Mr. Wolf," University of Kansas political science professor Burdett Loomis commented.