Smith has been Houston's general manager since 2006 following a stint as director of pro personnel with the Denver Broncos.
"We have a bond here with the coaching staff and the players and maybe it's because of all the things that we kind of had to deal with this year", O'Brien said earlier this week.
Smith said he wants to focus on his wife's recovery from breast cancer.
Erica Garner dies; fought police brutality after dad's death
His words became a rallying cry for Black Lives Matter protesters, and the video of the arrest made headlines around the world. Eric Garner died in 2014 after New York City police officers put him in a chokehold, a move the NYPD had banned.
With Smith stepping away, the need for Texans owner Bob McNair to choose between firing one or the other is mitigated. "This was an extremely hard decision for me to make as I love this organization and every member of this team bath on and off the field".
Another source speculated that Smith and O'Brien could keep working together but that it would be an "uneasy alliance" that's somewhat untenable.
Bill O'Brien, who had gained steam as a potential Giants contender were he to become available, "is likely to be back next season" as Texans coach, according to ESPN's Adam Schefter.
O'Brien's contract says he's in charge of who plays and doesn't play.
Lamar Jackson Struggles as Mississippi St. Beats Louisville in TaxSlayer Bowl
Jackson has yet to declare for the National Football League draft, but most outsiders believe the dynamic junior will turn pro. He ran 24 times for 158 yards and a touchdown, breaking the TaxSlayer Bowl record for most rushing yards by a quarterback.
Deshaun Watson has voiced his support for O'Brien.
Smith, in addition to trading up to draft Watson, has a solid record of first-round picks, including Watt, linebacker Jadeveon Clowney and receiver DeAndre Hopkins.
The Texans were apparently deliberating whether or not to fire O'Brien at the end of this season, but that doesn't appear to be the case any longer.
Notes on Nick: Foles struggles mightily against Cowboys
In a meaningless game played in freezing temperatures, the Eagles' inactives list was littered with precautionary deactivations. The Eagles should start fast in the first half, as their starters are more talented than what Dallas has to offer.