It is uncertain what Chudzinski's role will be with the Colts, but he'll likely help in a number of different areas, from practice to game planning.
"Rob and I have a long professional relationship and his résumé speaks for itself," Pagano said in a statement released by the team. "He brings a wealth of knowledge and will be a tremendous help to our entire team moving forward.
"Needless to say, we're excited to have 'Chud' joining our family."
Chudzinski and Pagano have plenty of history together. The two were part of the University of Miami's coaching staff from 1995-2000 and again with the Browns in 2004.
Chudzinski, who has 20 years of coaching experience, spent two seasons as offensive coordinator of the Carolina Panthers, who set team records for total yards (6,237) and first downs (345) in 2011.
Chudzinski helped Carolina quarterback and former No. 1 overall pick Cam Newton become the first rookie to throw for 4,000 yards.
Chudzinski coached the Browns for one season before being fired in December after posting a 4-12 record.
The offensive-minded Chudzinski will be reunited with Colts running back Trent Richardson, who was traded from Cleveland to Indianapolis this past season.