LOUISVILLE, KY. — Papa John’s International, Inc. has entered into a settlement agreement with founder John H. Schnatter, according to a March 4 filing with the Securities and Exchange Commission.

Papa John’s has agreed to cooperate with Mr. Schnatter to identify a “mutually acceptable” independent director who would not be affiliated with hedge fund Starboard Value LP or Mr. Schnatter, the filing said. If the new director is appointed to the board of directors before the 2019 annual meeting of shareholders, Mr. Schnatter said he will resign as a member of the board effective upon the independent director’s appointment. Otherwise, Mr. Schnatter’s term as a director will expire at the 2019 annual meeting.

Mr. Schnatter, who owns about 30% of Papa John’s shares, also has agreed to dismiss two lawsuits: one against the company in the Delaware Chancery Court without prejudice and one in Jefferson County, Kentucky, related to a sublease agreement with prejudice, the company said. Schnatter had filed several lawsuits against the company in an attempt to regain control.

The settlement agreement marks the end of a drawn-out battle between the pizza chain and its former chairman. The spat began in December 2017, when Mr. Schnatter stepped down as chief executive officer following comments he made against the National Football League leadership that garnered criticism.

Then, in July 2018, Papa John’s formed a special committee of the board of directors that terminated Mr. Schnatter’s founder agreement as the face of the brand after news surfaced that he used a racial slur during a May conference call.

But the dispute didn’t end there. In an Aug. 27 letter posted to his personal web site, Mr. Schnatter took aim at the company’s performance, saying that the source of its poor performance was due to “rot at the top.” In the letter, Mr. Schnatter voiced some of his sharpest criticism toward Steve M. Ritchie, new president and c.e.o. of Papa John’s.

However, Mr. Ritchie maintained optimism for the future of Papa John’s even after the company posted a loss of $13,033,000 in the third quarter ended Sept. 30, 2018, which compared with net income of $21,817,000 in the prior-year period.

“Our third-quarter results continue to reflect the brand challenges we have faced this year and were exacerbated by the negative impact of the media coverage that began on July 11,” Mr. Ritchie said during a Nov. 6 earnings call with investment analysts. “However, these events are not going to define the future of Papa John’s. During the quarter, we took important actions to help repair our brand reputation, and we believe good progress has been made. Our performance shows the positive impact from these efforts with improved consumer sentiment, third-quarter comp sales coming in better than our expectations, cash flows remaining strong and an improvement in North America comp sales outlook for the remainder of the year. As we continue working to rebuild trust, sustained consistent improvements and sales performance will take time.”