Coburn, a former congressman, captured 61 percent of the unofficial vote in Tuesday's primary to win the GOP nomination, the Oklahoman reported. Ex-Oklahoma City Major Kirk Humphreys was second with 25 percent of the vote despite Nickles' endorsement.
Carson easily won the Democratic senate nomination with more than 79 percent of the vote in a five-candidate race, according to unofficial returns from the state Election board.
The Coburn-Carson race will be watched closely in this year's race for control of the U.S. Senate. Oklahoma is one of only a few states with an open senate seat.
Candidates for U.S. House races were also nominated.
State Rep. Dan Boren, the son Oklahoma University President David Boren, won the Democratic congressional nomination in District 2, Carson's old district. He will face Republican Wayland Smalley.
Bert Smith won the Democratic nomination to face incumbent Republican Ernest Istook in the 5th District, and Republican John Sullivan will face Democrat Doug Dodd in the 1st District.