A person with knowledge of Joseph's deal told The Associated Press it was worth $48.75 million, with $23.5 million guaranteed.
The Texans went 6-10 last season and were desperate to land a top-tier cornerback. They further improved their secondary by signing safety Danieal Manning, a source told ESPN NFL Insider Adam Schefter, and reportedly were a front-runner to land cornerback Nnamdi Asomugha, a four-time Pro Bowler.
The 27-year-old Joseph is three years younger than Asomugha, and intercepted nine passes in his last two seasons in Cincinnati. The Bengals drafted Joseph out of South Carolina with the 24th overall pick in 2006.
The Texans open training camp on Sunday, and will get to work on shoring up the league's worst pass defense from 2010.
Houston allowed an average of 268 yards passing per game and 33 touchdown passes overall. Defensive coordinator Frank Bush was fired and Houston brought in Wade Phillips to install a 3-4 alignment.
The team used six of its eight draft picks on defensive players -- three on defensive backs. Phillips has said he plans to move 2010 sacks leader Mario Williams to outside linebacker and Glover Quin to safety.
But the Texans also needed an effective cornerback to shore up a secondary that gave up a league-high 18 receptions covering 40 yards or more. While Asomugha was considered the best free-agent cornerback available, Joseph has more interceptions (14) over the past five seasons than Asomugha (11).
Also Thursday, the Texans announced the signings of 15 undrafted free agents -- linebacker Mister Alexander (Florida State), guard Howard Barbieri (Rutgers), fullback Justin Bartlett (Carroll-Montana), linebacker Bryan Braman (West Texas A&M), linebacker Steven Friday (Virginia Tech), defensive end John Graves (Virginia Tech), punter Brett Hartmann (Central Michigan), offensive tackle Peter Hendrickson (Tulane), receiver Lester Jean (Florida Atlantic), receiver Jeff Maehl (Oregon), defensive end Zane Parr (Virginia), fullback Zac Pauga (Colorado State), safety Maurice Rolle (Louisiana-Lafayette), cornerback Jason Teague (TCU) and receiver Terrence Toliver (LSU). (LSU).
One of the Texans' main priorities now is re-signing All-Pro fullback Vonta Leach, the lead blocker for 2010 NFL leading rusher Arian Foster. Ralph Vitolo, Leach's agent, said this week that the Texans contacted him and expressed interest in bringing Leach back.
Information from The Associated Press was used in this report.