Davis, an undrafted free agent from East Carolina, was Matt Ryan's primary backup last year. He played in only game - at the end of a blowout loss at Tampa Bay.
The Falcons traded linebacker Akeem Dent to Houston late Wednesday night for Yates, a former fifth-round pick from North Carolina who started five of 13 career games after joining the Texans in 2011.
Yates is expected to battle Sean Renfree, a seventh-round pick from Duke last year, for the No. 2 job. Atlanta also has former Cornell quarterback Jeff Mathews, signed as an undrafted rookie last month, on the roster.