Brown's deal is for one-year, $3.5 million, and Smith's is for two years, $9 million, sources told ESPN NFL Insider Adam Schefter.
Brown was considered one of the better cornerbacks on the market, and his former team, the San Francisco 49ers tried to sign him prior to free agency starting.
Brown, 29, had a bit of strange season in 2013. He lost his starting job after he suffered a rib injury in November. But he regained his starting job in the playoffs.
Brown, a 49ers fifth-round pick in 2007, is considered a solid, fundamentally sound cornerback, who can be a good No. 2 starter. His career totals include 100 games played with 47 starts, 213 tackles and 11 interceptions.
Brown was involved in a strange situation last summer when he forfeited a $2 million workout bonus he was unaware of. His agent did not inform him of it and he fired the agent. In a show of good faith, the 49ers gave Brown a $300,000 bonus in December.
Smith set career highs with 6.5 and seven sacks in 2011 and '12. He earned a Pro Bowl nod for his 2011 season, a season during which the Texans won their first playoff game in team history.
He served a suspension that lasted two preseason games and the first regular-season game of 2013 for an on-field altercation with Dolphins guard Richie Incognito. The two players tangled and Smith ripped off Incognito's helmet and swung it. It was Smith's second confrontation with Incognito in two seasons and both resulted in discipline from the league for Smith.
The defensive end joined the Texans in 2009 as a free agent and renegotiated the deal in 2011.
Smith began his career with the Arizona Cardinals as a fifth-round draft pick in 2004.
ESPN.com Niners reporter Bill Williamson and ESPN.com Texans reporter Tania Ganguli contributed to this report.