Haslam got the nod from his fellow NFL owners in a Tuesday vote and told reporters at an introductory news conference Holmgren will step down at the end of season, handing over his duties to former Philadelphia Eagles president Joe Banner.
"With us coming in and taking a more active role, Mike has decided at the end of the year to leave the Cleveland Browns and retire," Haslam said. "Mike will work closely with us over the next four months to make this transition as easy as possible."
Haslam added Holmgren and Banner "will work together to transition, in a seamless fashion, to bring a winner to the Cleveland Browns."
Haslam in August agreed to buy a 70 percent stake in the Browns from Randy Lerner, who will still own 30 percent.
Holmgren, 64, has served as team president since December 2009, but the Browns have managed just 10 wins since then.
Banner resigned as the Eagles' president in June after running their affairs since 1995.