Bush's departure, expected for several days, was made official in a message sent to the program's staff Monday by Noah Oppenheim, the executive in charge of "Today."
"Billy Bush will be leaving the 'Today' show's 9 a.m. hour, effective today," Oppenheim wrote. "While he was a new member of the TODAY team, he was a valued colleague and longtime member of the broader NBC family. We wish him success as he goes forward."
In a statement, Bush said: "I am deeply grateful for the conversations I've had with my daughters, and for all of the support from family, friends and colleagues. I look forward to what lies ahead."
Bush, 45, was suspended indefinitely Oct. 9, after he was heard in a leaked 2005 video engaging in sexist banter with Trump. The existence of the tape has been a major headache to NBC since it was revealed by the Washington Post on Oct. 7.
The settlement is an expensive attempt to make the controversy go away. Bush is probably leaving with whatever he was owed on his contract, which was said to earn him $2 million to $3 million annually, according to people familiar with the terms of the deal. Bush's attorney Marshall Grossman has reportedly been seeking a settlement since the middle of last week.
In the provocative tape, made while Bush was co-host of NBC's syndicated news magazine "Access Hollywood," Trump obscenely boasts about his ability to kiss women and grope their genitals with impunity because he is a celebrity. Bush is heard chuckling and encouraging Trump's coarse chatter even as the reality show star crudely talked about how he tried to have sex with Nancy O'Dell, then a co-host on "Access." Bush is also seen telling "Days of Our Lives" soap opera actress Arianne Zucker to embrace Trump just after the exchange.
Bush issued an apology for his behavior, saying he was "younger, less mature and acted foolishly in playing along."
But the negative reaction to Bush's role in the explosive campaign revelation, focusing attention on Trump's history of alleged inappropriate behavior with women, was untenable for NBC News going forward.
Although some members of NBC News management were willing to forgive Bush, there was concern the "Today" audience would reject him. Some female staffers at "Today" also made it known to their bosses they would be upset if Bush returned.
Bush had been a co-host on the 9 a.m. hour of "Today," in which 68% of the 3 million viewers who watch are women.
4:30 p.m.: This story was updated to include Billy Bush's statement.