The 45-year-old has signed a three-year deal with the Championship side.
Portsmouth chief executive David Lampitt is confident Cotterill is the right man for the job.
“Steve is the perfect fit for the rebuilding job we want to do here,” he told Portsmouth’s official website.
“He’s talented, ambitious, energetic and positive, with a very good footballing CV, coming here on the back of a great achievement at Notts County.
“We’ve got lots of challenges ahead and like the rest of us here at the club Steve is ready to tackle them head on to bring stability and long-term success to Pompey.”