The comic writer, director and producer was presented with the honour by Prince Charles.
Speaking afterwards, The Daily Telegraph reports that Iannucci described the investiture ceremony as "slightly surreal, a little bit hilarious" but "also quite moving".
He added: "I've just been doing my job for the last 20 years and quite enjoying it and it's very nice to get that recognition, but there are a lot of people here who have put in years of dedication to their local communities."
Iannucci also commented on his Twitter spat with Alastair Campbell regarding his decision to accept the OBE, joking that it only happened because he had been left home alone by his wife.
Iannucci has been behind some of the most acclaimed British comedy series of the last 25 years.
After coming to prominence with Chris Morris and Steve Coogan in the groundbreaking radio show On the Hour and its TV equivalent The Day Today, his later work has included I'm Alan Partridge, The Thick of It and most recently Veep.
He also directed The Thick of It spin-off movie In the Loop, and is a co-writer on the upcoming Alan Partridge Movie.
Watch Armando Iannucci discuss The Alan Partridge Movie with Digital Spy below: