McGrady, a seven-time All-Star, spent last season with Detroit and over 72 games he averaged 8.0 points, 3.5 rebounds and 3.5 assists per game.
The ninth-leading active scorer in the NBA with 18,108 points, he has played in the NBA since the 1997-98 season.
Over 886 games with Toronto, Orlando, Houston and Detroit, he has averaged 17.1 points, 3.9 assists and 3.0 rebounds per game.
Collins will be entering his third season with Atlanta and 10th in the NBA. He has averaged 3.9 points and 4.0 rebounds over 645 games with New Jersey, Memphis, Minnesota and Atlanta.
Also on Friday, Atlanta signed center Keith Benson, its second-round draft pick (48th overall) out of Oakland University where he averaged 14.1 points, 8.2 rebounds and 2.7 blocks over 135 games.