Veteran TV journalist Rose, 76, was sacked by CBS in November after being accused by more than 10 women of sexual misconduct.
The announcement, from CBS News president David Rhodes on Tuesday, comes more than a month after Rose was sacked from the network amid allegations of sexual misconduct.
Dickerson, now host of the long-running Sunday public affairs show "Face the Nation", will "transition off" that program in the coming weeks, then a successor will be named, according to CBS.
Dickerson will join Gayle King and Norah O'Donnell on the critically acclaimed and award winning broadcast. "I have behaved insensitively at times, and I accept responsibility for that, though I do not believe that all of these allegations are accurate", Rose said in a statement shortly after the disclsoure".
The move the latest in a series of on-air changes at CBS News. In 2015, he took over the "Face The Nation" role from legendary newsman Bob Schieffer.
"Every time I've been on the show, I haven't wanted the conversation with Norah and Gayle to end when my segment does", Dickerson said.
Rhodes said in his memo that he'll be in Washington later this week to begin the process of finding Dickerson's replacement there. "He's the flawless complement to Gayle and Norah and will help us continue the momentum CBS This Morning has achieved over the last six years".
Dickerson joined CBS News in April 2009 as an analyst and contributor to all of the network's broadcasts and platforms. He will continue hosting Face the Nation at least through the weekend as Rhodes and executive producer Mary Hager determine what's next for the Sunday show. "CBS This Morning" is in its closest competitive position with "Today" in at least three decades and in almost two decades.
Houston police: Missing journalist found, appears unharmed
She said he drove a blue truck and pulled up behind her in her driveway, but drove off after she got out of her vehicle . In a facebook post Sunday, friends and family pleaded for the public's help in finding a Texas A&M football reporter.
Donald Trump Plans to Attend World Davos Economic Forum
Trump's inauguration, becoming the first Chinese leader to mingle with the corporate and media crowd in the mountain village. The Global Economic Forum was founded in 1971 by Klaus Schwab, a business professor at the University of Geneva.