The Paul campaign turned in paperwork and a $500 check to the secretary of state's office this afternoon, the Associated Press reports. Paul is running as a Republican.
He has reportedly already raised $1.7 million for his run, largely from people who supported his father's failed bid for the GOP presidential nomination last year.
On his Web site, Paul says he believes "America can prosper, preserve personal liberty, and repel national security threats without intruding into the personal lives of its citizens."
Echoing his father, Paul adds that "for too long the Federal Reserve has operated behind a shroud of mystery—as Senator I would make sure that all Americans understand the dangers of unsound monetary policy and shed light on this secretive organization."
Paul, an eye surgeon, is seeking the seat now held by retiring Republican Sen. Jim Bunning. He is believed to be a serious contender in the race for the GOP nomination, which also includes secretary of state Trey Grayson.