Robinson, who spent six seasons with the Texans, received a $57 million deal, a source with knowledge of the situation said. Robinson is guaranteed $22.5 million.
Robinson was the 10th overall draft pick by the Texans in 2004. He had six interceptions as a rookie.
The Falcons, who ranked 28th in the NFL in pass defense in 2009, targeted Robinson awhile ago and seized the opportunity to nab the best cornerback in free agency. Atlanta's smallish corners were targeted last season, and Robinson adds size and better coverage ability than any defensive back on the roster.
The Associated Press contributed to this report.