David Canter, Dobbins' agent, confirmed the new deal Wednesday in a text message after announcing it on Twitter.
The 6-foot-1, 236-pound Dobbins played in 14 games last season and started five after Brian Cushing sustained a season-ending knee injury in October. He was also a special teams captain and made 43 tackles and intercepted a pass in 2012, his second season with the Texans. Dobbins missed the playoffs with an ankle injury.
Dobbins joins tackles Andrew Gardner and Ryan Harris and cornerback Brice McCain as unrestricted free agents who've re-signed with Houston. The Texans have also signed safety Ed Reed, punter Shane Lechler and fullback Greg Jones.