Other media outlets also reported that O'Brien was joining Houston. An introductory press conference is reportedly scheduled for Saturday.
The Texans fired coach Gary Kubiak in early December, and they finished the season with 14 consecutive defeats. After going 2-14, Houston will make the first pick in this year's NFL Draft.
Before coaching the Nittany Lions the past two seasons, O'Brien was an assistant coach with the New England Patriots for six years and the offensive coordinator when they lost to the New York Giants in Super Bowl XLVI.
He took over in State College in the wake of the Jerry Sandusky sex-abuse scandal and managed to keep the Nittany Lions competitive despite NCAA sanctions.
O'Brien, 44, guided Penn State to 15-9 record. He was selected Big Ten coach of the year after the Nittany Lions finished 8-4 in 2012.
O'Brien interviewed for the Philadelphia Eagles and Cleveland Browns head coaching jobs last offseason. Penn State made it easier for O'Brien to leave for the NFL by reducing the buyout teams would have to pay the school for hiring him from $19.33 million to $6.48 million.
Wade Phillips took over as the Texans' interim coach after Kubiak was fired following the team's 2-11 start. Houston lost all three games under Phillips as part of the longest losing streak in franchise history.
Houston becomes the first NFL team to hire a new coach in the offseason. Five other teams fired their coaches Sunday or Monday, but the Texans had a head start on the search process after relieving Kubiak of his duties in-season.