The Bills released Byrd on Sunday.
The Commanders released Byrd on Wednesday.
Byrd signed with Houston's practice squad Wednesday.
Byrd didn't record a catch on two targets during Sunday's 31-28 loss to the Vikings.
The Falcons promoted Byrd to their active roster Saturday, D. Orlando Ledbetter of The Atlanta Journal-Constitution reports.
The Falcons signed Byrd to their practice squad Thursday, Tori McElhaney of the team's official site reports.
Byrd caught 13 of 23 targets for 268 yards and two touchdowns across 14 appearances during the 2022 campaign.
Byrd caught one of two targets for 12 yards during Sunday's 20-19 victory over the Cardinals.
Byrd caught his only target for 12 yards during Sunday's 19-16 loss against Pittsburgh.
Byrd gathered in both of his two targets for 29 yards during Sunday's 27-24 win versus Chicago.