Rose was sacked by CBS and other employers in November after the Washington Post reported on a series of harassment allegations in Rose's past. During the 2016 presidential campaign he moderated CBS News' two presidential debates and as host of FACE THE NATION, interviewed each of the major candidates multiple times.
Dickerson has anchored Face the Nation for over two years, as it generated some of its largest audience levels of the past three decades.
He will join Norah O'Donnell and Gayle King on the morning show.
Rose apologized "for my inappropriate behavior" and said "I am greatly embarrassed".
Don't Expect OPEC's Oil Deal To Fall Apart in 2018
Adding to the positive sentiment, analysts expect global economic growth to lead to higher demand for oil. Iran said on Tuesday that OPEC members were not keen on increased prices.
"Few people possess John's intellect, curiosity and journalistic chops", Ryan Kadro, executive producer of "This Morning" said in a statement. "Gayle and Norah continue to show tremendous leadership on our morning broadcast each day".
By naming Dickerson, a veteran Beltway journalist who often provides historical analysis in his coverage, CBS News is sending a signal that its morning program will retain its positioning as a hard-news alternative to the other broadcast networks' offerings in that time slot.
Tuesday happens to be the six-year anniversary of "CBS This Morning". Most recently, he was Slate Magazine's chief political correspondent winning the Ford Prize for Distinguished Reporting on the Presidency.
Dickerson will begin Wednesday, and will relocate to be in NY full-time. But with "CBS This Morning", the network is in a better competitive position against "Today" and "GMA" than ever before. While "CBS This Morning" trails rivals "Today" and "Good Morning America" on NBC and ABC, respectively, in viewership, it has made significant ratings strides for CBS with a mix of hard-news focus and serious discussion about the headlines of the day.