"I am extremely proud of our accomplishments during the past five years and have full confidence in the leadership at Qwest," Notebaert said. "The time has come for me to spend more time with family and focus on other commitments.
Notebaert, chairman and chief executive for five years, said he would step down "only when the board has selected a leader who shares our vision and will continue to guide Qwest's solid performance and reputation as a leading national communications provider with a very bright future," The Wall Street Journal reported Monday.
The company said a formal search was under way but a timetable for naming a successor has not been determined.
Notebaert took over the company when it was on the verge of bankruptcy, caught in an accounting scandal and overburdened with debt. Many people have credited the company's turnaround to Notebaert, whose no-nonsense style lead to improvements in the company's accounting practices.