Owens decided family was more important than national office, and will instead finish out his second term, which ends in 2006, sources close the governor said on condition of anonymity. Owens scheduled a news conference for later Tuesday.
Campbell, 70, announced abruptly last week that he would not seek re-election, citing declining health. He was treated for prostate cancer last year. His Washington office also faces allegations that a longtime aide had taken kickbacks.
Campbell's seat had been considered safe for the GOP, which holds a 51-48 margin in the Senate. His decision gave Democrats another open Senate seat to target in November and threw the Colorado Senate race wide open.
GOP officials had urged Owens to run for the seat, saying recent polling showed him the best candidate against five relatively unknown Democrats now in the race.
The GOP lacks a high-profile candidate, though Reps. Bob Beauprez, Tom Tancredo and Scott McInnis have all said they are interested in the job.
Two prominent Democrats, including Colorado Attorney General Ken Salazar and Rep. Mark Udall, have said they are considering running.
Former Democratic Sen. Gary Hart has indicated he will not run.