ABC News President Ben Sherwood moved quickly to replace him, appointing Amy Robach as the "Good Morning America" news anchor.
Elliott follows former "GMA" weather forecaster Sam Champion out the door. Champion joined the NBC Universal-owned The Weather Channel, where he began a morning show of his own earlier this month.
Now that it is No. 1 in the morning, ABC has been involved in delicate negotiations to keep intact the team that got it there. Roberts recently signed a new contract to stay at "GMA," and co-host Lara Spencer finalized a new deal last week. Co-anchor George Stephanopoulos and new weather forecaster Ginger Zee also are part of the show's cast.
ABC took the top spot from NBC's "Today" show two years ago. The addition of Elliott and Spencer was a key move in the show's ascendancy, with the chemistry of ABC's morning team a major selling point when "Today" was hurt by the bad vibes surrounding Ann Curry's departure in 2012.
At NBC, Elliott will work on Sunday night football, the Olympics, horse racing and other events, spokesman Greg Hughes said. A formal announcement is expected later this week. Financial terms were not disclosed.
Sherwood said, "As many of you know, we have been negotiating with Josh these past several months. In good faith, we worked hard to close a significant gap between our generous offer and his expectations. In the end, Josh felt he deserved a different deal and so he chose a new path,"
Elliott did not immediately respond to requests for comment.
No role has been set for Elliott in NBC's news department. But restoring the "Today" show to its former luster is a top priority at Comcast Corp.-owned NBC, and weakening its chief competition by poaching Elliott may be part of that strategy. Another ABC News personality, "Nightline" host Cynthia McFadden, also accepted a job at NBC last week.
Robach, who used to work at NBC, is familiar to ABC's morning audience since she filled in for Roberts after the host underwent a bone marrow transplant. Robach, who has been battling breast cancer, was assigned by ABC to cover the Winter Olympics in Sochi.
"Amy will be a fierce and formidable full-time addition to our GMA team," Sherwood said in a memo to ABC News staff on Sunday.
Morning television is the most lucrative time of day for broadcast network news divisions, increasing the importance of personnel moves at their shows.