Richardson, 81, has owned the team since it entered the NFL ranks in 1995. He announced in December that he was selling the team, after the NFL announced an investigation into allegations of workplace misconduct against him.
He was fined $2.75 million in June as a result of the investigation.
"We are grateful to the Carolina community for the love and support you have shown your Panthers," Richardson wrote in his letter. "Your enthusiasm for football and devotion to the team has been a source of strength for us and for everyone who calls the Carolinas home."
Richardson also played for the Baltimore Colts in 1959 and 1960. He was a 13th round NFL Draft pick.
"It's been almost 60 yards since I last took the field, and I know how tough it is to play this game," Richardson said. "I have the highest respect for the men who wear the Panthers jersey. You inspire me every week with your commitment and your determination to win. I will always be your No. 1 fan."
"I wish Mr. Tepper all the best: the team is in good hands. The stadium is a wonderful place to watch a game with friends and family. Carolina is and will be a contender. From the thousands of people who come every year to training camp to the millions of fans who come to the stadium or follow the team every day, we thank you for making a home for Panthers football in your hearts."
Panthers COO Tina Becker also resigned on Monday.
Tepper is the founder and president of global hedge fund Appaloosa Management, L.P. He signed a definitive agreement to purchase the Panthers on May 16. NFL owners approved the purchase on May 22.
"I am thrilled to begin this new era of Carolina Panthers football and am humbled by the overwhelming excitement and support for the team," Tepper said.
"On behalf of the fans and myself, I thank Jerry Richardson for bringing the team to the Carolinas and for entrusting me with its future. Winning is the most important thing both on the field and in the community, and I am committed to winning a Super Bowl championship together. I look forward to being part of the Panthers' family and to supporting this flourishing region."
Jerry Richardson's farewell message pic.twitter.com/jHhaO6YxaV— Carolina Panthers (@Panthers) July 9, 2018
The Panthers report to training camp on July 26 at Wofford College in Spartanburg, S.C.