The Houston Chronicle reported Wednesday that O'Brien will sign a five-year deal and be introduced by the team Thursday. Penn State held a news conference Thursday in which it acknowledged O'Brien's departure.
Texans owner Bob McNair wanted a coach who had NFL and head-coaching experience.
O'Brien, 44, a protégé of Bill Belichick, was a New England Patriots assistant from 2007 to 2011. He eventually became the offensive coordinator for a team that lost to the New York Giants in Super Bowl XLVI. He left the Patriots two years ago to take over at Penn State in the wake of the Jerry Sandusky sexual abuse scandal.
Despite a bowl ban and relaxed transfer rules that allowed players to leave Penn State without delay, the Nittany Lions went 15-9 under O'Brien, including 10-6 in the Big Ten. He was the conference coach of the year in 2012.
Defensive line coach Larry Johnson Jr. will assume O'Brien's duties on an interim basis until a new Nittany Lions coach is hired.
Johnson is the last remaining assistant from Joe Paterno's staff and has coached in Happy Valley for 18 seasons. He's long been known as a hard-nosed recruiter and has helped develop seven first-team All-Americans.
The Texans were the first NFL team to create a coaching vacancy this season when they fired Gary Kubiak on Dec. 6, and they're the first to make a hire.
Despite Super Bowl aspirations and what McNair called the most talented roster he'd ever had, the Texans went 2-14 -- despite a 2-0 start -- after winning back-to-back AFC South titles the previous two years.
Defensive coordinator Wade Phillips took over as interim coach once Kubiak was fired, and he was one of three candidates the Texans interviewed for the position, along with O'Brien and former Chicago Bears coach Lovie Smith, who did not coach in 2013 after being fired following the 2012 season.
Now, Phillips wonders if he'll remain on the staff.
"I don't know what their feeling is, not knowing the guy," Phillips was quoted as saying. "Usually, when somebody gets a job and you don't know anything, you're probably not involved. But I don't know that for a fact."
O'Brien met with the Texans the week after Christmas at his home on Cape Cod in Massachusetts, sources said.
As a condition to returning to Penn State in 2013, O'Brien and the school had agreed to an amended contract that lowered his buyout to join an NFL team from $19.33 million to $6.48 million. There had been conversations to further reduce the NFL buyout.
Incoming Penn State recruit Thomas Holley, the school's second-highest ranked recruit in 2014, told ESPN.com that he had a conversation Saturday with O'Brien, who told the defensive lineman that he was staying with the Nittany Lions.
However, Holley backtracked from those comments on Sunday.
The Texans will pick first overall in the 2014 draft and are expected to target a quarterback.
ESPN's Adam Schefter and Chris Mortensen and ESPN.com's Tania Ganguli and Tom VanHaaren contributed to this report.