Lambert has been appointed as Paul Hurst's successor at Ipswich Town on a contract until 2021.
Hurst, the former Grimsby and Shrewsbury boss, was sacked on Thursday after just one win from 14 Championship games since being appointed in May.
Lambert, taking his first job since being sacked by Stoke, is tasked with lifting the Portman Road club off the foot of the table.
The Scot said: "I can't wait to get going and I'll be using all my experience - and give everything I've got for Ipswich Town.
"I know about the history of the Club, what a fantastic football club it is and I'm proud to be the manager here."