Millwall appoint Rowett as manager
Rowett takes over from Millwall legend Neil Harris, who resigned earlier in October after four and a half years at The Den.
The 45-year-old was chosen by Lions owner John Berylson after the American flew into England to carry out interviews.
Rowett began his managerial career at Burton before spells at Birmingham and Derby.
He led Derby to the Championship play-offs in 2017-18 before his disappointing spell with Stoke.
He was sacked by Stoke in January, having won only eight of 26 league matches following the Potters' relegation from the Premier League.
Caretaker manager Adam Barrett will oversee Tuesday's game against Cardiff, with Millwall sitting 17th in the Championship after blowing a two-goal lead in the final minutes of Saturday's 3-2 defeat at Brentford.
Rowett's first match will offer a chance for revenge against Stoke at The Den on Saturday.
"It's incredibly exciting after eight months out of the game," Rowett told Millwall's official website.
"Just feeling that buzz again really and being desperate to be back part of it. Getting an opportunity at a club like this - a really, really passionate club with a great history - for me that's what it's all about and I can't wait to get started."