The promotion is expected to be announced this week, according to the newspaper. In addition to co-hosting the NBC morning show's third hour — where he replaces the recently promoted Savannah Guthrie — Geist will serve as a backup for Matt Lauer.
Geist, 37, will still maintain a presence on Morning Joe, but he will no longer host Morning Joe's predecessor Way Too Early.
Geist initially came to MSNBC as a producer for Tucker Carlson's show before taking an on-air role on Morning Joe. He began filling in for various members of the Today ensemble in 2010.