Hamilton was Andrew Luck's offensive coordinator during the quarterback's senior season at Stanford.
"I am thrilled to have Pep as our new offensive coordinator," Colts coach Chuck Pagano said in a statement released by the team. "He's had success everywhere he's been and his familiarity with guys like Andrew and Coby will make him a great fit for our team. I can't wait to start working with him as we get ready for next year."
In Luck's statement, the quarterback thanked Arians for his time, while welcoming Hamilton.
"First of all, I'm very happy for coach Arians and I wish him nothing but the best in Arizona," Luck said. "I really enjoyed working with him this season, and I'm very thankful for all of his guidance. I'm thrilled to be able to reunite with coach Pep here in Indianapolis. He was a tremendous mentor of mine at Stanford and he is going to have our offense playing at a high, energetic level."
Hamilton spent time with the Baltimore Ravens, New York Jets, San Francisco 49ers and Chicago Bears before being hired to coach receivers at Stanford in 2010. He was promoted to offensive coordinator/quarterbacks coach in 2011. Luck was the runner-up in Heisman Trophy voting that season before being selected first overall by the Colts last April.