The 60-second film, created by 4Creative, was made for E4 and features a host of TV personalities including The Crystal Maze presenter Richard Ayoade and Made in Chelsea stars Ollie Locke, Oliver Proudlock and Frankie Gaff.
The ad consists of the participants reminiscing on their "first times", examples of which took place in a library, in a primary school and in a village hall.
It was co-directed by Iannucci, whose creations include The Day Today, I’m Alan Partridge and Veep, alongside John Pape.
The spot, which will run on E4 until election day on 8 June, was created by 4Creative's Will Clark.
Channel 4’s head of marketing James Walker said: "We’re thrilled that Armando came on board with this project.
"We wanted a film that would entertain but also carry a serious message – exercising your democratic right to vote is one of the most important things anyone can do but getting that message across without being too worthy or dry is a really difficult challenge, but 4Creative and Armando have cracked it."