Rodgers, who appeared on a celebrity edition of the show in 2015, first announced the news during his weekly appearance on The Pat McAfee Show. He later apologized for letting it out, saying he "jumped the gun" on the announcement.
"I may have jumped the gun a little bit, so I apologize to Jeopardy! if they wanted to announce it," Rodgers told reporters Tuesday. "I just got so excited on the show earlier. It just went down the last couple of days, us figuring it out. It is very exciting.
"It's for the off-season. We'll be even more excited when that opportunity gets a little closer, but the show has been so special to me over the years. It's been a staple at my house here in Green Bay for the last 16 years -- six o'clock watching Alex [Trebek] and trying to get as many questions as I can."
Trebek, the longtime host of Jeopardy!, died of cancer at age 80 on Nov. 8.
"When the opportunity came up [for Celebrity Jeopardy!] in 2015, I mean that was a dream come true to be on there," Rodgers said. "To get to meet Alex was just such a special moment, and we're all obviously sad about his passing.
"There's this nostalgic connection to certain figures in our life based on our childhood and where we were at and the times we had those memories. It almost makes these people feel like family, like you know them."
Rodgers currently is preparing for Saturday's NFC divisional-round game against the Los Angeles Rams. The Packers are scheduled to play the Rams at 4:35 p.m. EST at Lambeau Field.