Despite an impressive victory over France in this year's Six Nations, Mallett had achieved just six victories in 36 Tests with the Azzurri, who will not renew his contract.
Brunel has previously worked at Les Blues as assistant coach under Bernard Laporte and helped them to World Cup semi-finals in 2003 and 2007.
At Perpignan, he led the club to the league title in 2009 as well as the Top 14 final last year but they fell short in the Heineken Cup semi-finals against Northampton.
The new deal, in what he has claimed will be his last job, will take Brunel through to the 2015 World Cup in England and he revealed he couldn't wait to begin his new role.
"I want to thank (FIR) president (Giancarlo) Dondi and the whole Italian Rugby Federation for this extraordinary possibility they have offered me," he said.
"Italy is now a great rugby-playing nation, they have played in the Six Nations for more than 10 years and with their participation in the Celtic League they can continue to take steps forward.
"I will study the national team and Italian rugby over the next few months from afar, paying special attention to how the Azzurri get on at the World Cup.
"And from the end of the tournament in New Zealand I will start to work directly with the team."