Stephenson tweeted that he was looking forward "to the next phase of my career and the wonderful opportunity to continue to grow as a player and as a person in Charlotte!"
US sports broadcaster ESPN reported that Stephenson has signed a three-year, $27 million contract with the Hornets that includes a team option for the final season.
The 23-year-old Stephenson reportedly turned down a five-year, $44 million deal from the Pacers.
Stephenson was slapped with 14 technical fouls during the regular season. He was fined twice for flopping during the Eastern Conference finals where he also got into a tussle with teammate Evan Turner during a practice.
Stephenson averaged career highs in points (13.8), rebounds (7.2), assists (4.6) and minutes (35.3) in 78 games this past season.
"Indy, I had a great 4 years," Stephenson wrote on Twitter. "Thank you Larry Bird, the fans, my coaches and teammates for the incredible experience.
"I will never forget any of you!"
He has career averages of 9.1 points, 4.4 rebounds and 3.1 assists across four seasons with Indiana.