Gregory is an NBC News correspondent and the host of an hourlong weekday show on MSNBC.
The switch comes following months of criticism of Olbermann and Matthews and claims that their on-air work reflects a partisan political bias. The criticism escalated after Olbermann and Matthews worked as dual anchors for the cable network's coverage of the Democratic and Republican conventions.
The change is directly attributable to what the Times called tensions arising out of a widespread perception that MSNBC has become politically liberal.
MSNBC President Phil Griffin told the Times MSNBC ratings have been an "incredible success."
However, current and former NBC employees said long-running friction between NBC and MSNBC reached a breaking point during the conventions.
"MSNBC is behaving like a heroin addict," a senior staff member told the Times. "They're living from fix to fix and swearing they'll go into rehab the next week."