The show has run for four series with a pair of specials between the second and third, and the final episode of the current run will air this weekend.
Iannucci told The Guardian: "It's definitely the last series. I've known from past experience to never say never.
"I don't think it's going to change politics. In terms of comedy hopefully it will inspire someone in the same way that I remember listening to Hitchhiker's Guide to the Galaxy or watching Not the Nine O'Clock News and thinking, 'I want to do something like that'."
Writer Sean Gray added: "It's a shame to stop but it also makes sense because hopefully we haven't outstayed our welcome.
"It's great to leave at a point where people are hopefully wanting more. That's the best way."
Various members of The Thick of It team including Chris Addison had previously confirmed on Twitter that the show would end with the fourth series finalé.
The seventh and final episode in the fourth series of The Thick of It airs this Saturday (October 27) at 9.30pm on BBC Two.