This comes in the wake of his role in a lewd 2005 conversation with presidential contender Donald Trump about women.
This comes in the wake of his role in a lewd 2005 conversation with Republican presidential contender Donald Trump about women.
Bush, 45, has been suspended from hosting duties on NBC's flagship morning show after the emergence of the tape, in which Bush and then reality star Trump, joked and boasted about groping women.
In a statement on Monday, Bush said he was "deeply grateful for the conversations I've had with my daughters, and for all of the support from family, friends and colleagues."
NBC's memo said, "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."
No further details were given regarding a financial settlement.
In the 2005 video, Bush was heard laughing and joking with Trump, who bragged about grabbing and kissing women and trying to seduce a married woman.
The video was made as part of a segment for "Access Hollywood," a celebrity and entertainment news program that is also part of the NBC group.
Bush, a cousin of former U.S. President George W. Bush, became one of the co-hosts of the "Today" show in August. The morning show is one of NBC's most lucrative properties and boasts a large female viewership.
He apologized on Oct. 7, saying he was "embarrassed and ashamed" by his behavior, and NBC announced it was suspending him from "Today."
Noah Oppenheim, the executive in charge of "Today" had written in a memo to staff that "there is simply no excuse for Billy's language and behavior on that tape."
The married woman discussed in the conversation has since been identified as Bush's "Access Hollywood" co-host Nancy O'Dell.
Last week, O'Dell said that there is "no room for objectification of women, or anyone for that matter, not even in the locker room."