The two-year deal is worth $2.7 million and includes $450,000 in guaranteed money, sources said.
Clemons, who turns 29 in September, spent the first five years of his career with the Dolphins. He was a fifth-round draft pick in 2009, back when Brian Gaine, the Texans' director of pro personnel, was with Miami. He started all 16 games for the Dolphins in 2012 and '13, during which time he caught three interceptions and made 191 tackles.
Clemons visited Houston on Friday.
Among the safeties currently on the Texans' roster is veteran Danieal Manning, who was signed to a four-year, $20 million deal in 2011. Manning, who is due $4.5 million, with a salary cap charge of $6 million, for 2014, was asked by the team to take a pay cut in the final year of his contract, sources said.
Clemons' salary with the Texans will be similar to the salary offered to Manning in his pay cut.