The two shared a moving moment after O'Connell apologized to Wheaton for not being aware of the childhood abuse he had suffered.
The "Stand by Me" actor will be the daytime talk show's first full-time male co-host.
"A gentle nudge in the right direction is so much better than a public execution,” the TV personality said in a recent interview.
The co-host's announcement continues a tumultuous season for the daytime chat show.
CBS said that Osbourne's behavior toward her co-hosts during the March 10 episode "did not align with our values for a respectful workplace.”
"We will miss her humor, kindness and good nature," CBS said.
Toasts and hugs all around for a familiar face who succeeds Julie Chen on the CBS chat show.
Osbourne said her former "The Talk" colleague Julie Chen, who's married to Moonves, will "probably hear this and hate me, but I have to tell the truth."
The co-host will address her departure in a video message on Tuesday's episode.
Co-host Julie Chen, who is Moonves' wife, did not appear on Monday's show.