Iannucci, 51, said he will exist the HBO comedy in its fifth season, adding he was happy to go out on top, reported Entertainment Weekly.
"Like Italian tennis players who bow out as soon as they win the Open, I think this is a good course to follow...
"I just felt that I took the show to where I wanted to take it, and I'm pleased to pass it on and challenge Dave Mandel ('Curb Your Enthusiasm' alum) to sort out the constitutional issue that we've dumped on his floor," he said.
"Veep" broke the winning streak of "Modern Family", which was up for a record sixth award in the category.
"I think it feels like the right time. Every show can benefit from new energy and new names and new ideas, and what better time to do that? So I think it feels right.
"We've made history by being the first time 'Veep' has won Best Comedy. And so in many ways, the tradition is maintained," Iannucci said.