Stoke sacked Hughes nine days ago, just hours after an embarrassing FA Cup exit at the hands of Sky Bet League Two club Coventry and with the Potters mired in the top-flight relegation zone.
Derby’s Gary Rowett, Espanyol’s Quique Sanchez Flores and Republic of Ireland boss Martin O’Neill were all considered targets but the former signed a new contract last week and over the weekend the other two ruled themselves out of contention.
Lambert, who has previously managed Wolves, Blackburn, Aston Villa and Norwich, emerged as the preferred candidate and the club have acted swiftly to appoint him.
“When the club made a managerial change nine days ago we stated that we were looking to make an appointment as soon as possible, particularly given our position in the league and the overriding priority being retaining our place in the Premier League,” said a Stoke statement.
“The club reviewed a number of people against the criteria set and met with a small number of parties who had expressed an interest in the job.”
Vice-chairman John Coates said it was imperative the new manager had Premier League experience.
“We were determined to appoint someone with Premier League experience or an extensive knowledge of English football,” he said.
“Paul has been successful in management at clubs with a strong and stable background and with local ownership - the kind of foundation we are able to give to our managers.
“We look forward to working with Paul and supporting him to help achieve our goals.”