Clarkson will play Ron Swanson (Offerman)'s first ex-wife Tammy 1 in two episodes of the upcoming fourth season.
Offerman told reporters earlier this week: "I've been such a huge fan of hers for many years, and it's nothing short of a dream come true that I got to actually work in scenes with her.
"She even surpassed our expectations. Not only is she gorgeous and an incredible actress, but she is insanely hilarious to boot. I think everybody on set was just bowled over with how funny she was on the show."
Show co-creator Michael Schur dropped hints about the character of Tammy 1, revealing that she is "very different" to Tammy 2 (Megan Mullally).
"The relationship she has with Ron is not a hedonistic animal attraction that we've seen before," he added. "They have a more complicated and rich backstory that we get into and delve into."
Schur recently said that former regular cast member Paul Schneider may reprise his character Mark Brendanawicz in a couple of episodes if the scheduling can be worked out.
Parks and Recreation returns for its fourth season on September 22 in the US.
> Parks and Recreation interview with Nick Offerman and Michael Schur
Watch Tammy 1 mentioned in the Parks and Recreation third season finale: