Dampier, 36, bolsters the team's roster for a tough stretch that begins with a game against Dwight Howard and the Magic on Friday night. The challenges continue with a game against the Miami Heat on Sunday and a visit to the Lakers on Tuesday.
The game against the Lakers is the first of a five-game road trip that also includes games at Phoenix, Portland, Chicago and New York.
Hawks coach Larry Drew said he needed another big body "particularly with the schedule the next couple of weeks being what it is."
Horford, an All-Star last season, was lost for at least three months with a torn pectoral muscle last month. He may not return before the playoffs.
Collins, a backup center, sprained his left elbow last week. Collins, who has called the injury a "moderate" sprain, is expected to miss at least another week.
The injuries left Zaza Pachulia as the only true center on the roster. Ivan Johnson, a 6-foot-8 undrafted power forward, has been playing behind Pachulia but lacks the size to match up against centers such as Howard and the Lakers' Andrew Bynum.
Dampier was selected 10th overall by Indiana in the 1996 NBA draft. He has played in 972 regular season games and 57 playoff contests with Indiana, Golden State, Dallas and Miami.
Dampier appeared in 51 games last season for the Heat, averaging 2.5 points per game and 3.5 rebounds.