"It was a difficult decision in 2002 to not come then but to be here as manager is fantastic.
"I'm delighted, I've got a right buzz, I just can't wait to see the stadium full of the passionate fans we have.
"We want to get back in the Premier League, I'm under no illusions of how tough it will be but that would be our aim."
Pompey chief executive David Lampitt welcomed the arrival of Cotterill, saying: "Steve is the perfect fit for the rebuilding job we want to do here.
"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."
Cotterill began his managerial career at Sligo Rovers, before guiding his hometown team Cheltenham into the Football League in 1999.
He then had spells at Stoke and Sunderland, where he was assistant manager to Howard Wilkinson, before taking charge of Burnley for three years.
Cotterill joined Notts County on a short-term contract in February and guided them to the League Two title, overseeing 14 wins and one defeat in his 18 games in charge and conceding only six goals during that spell.
But the former Bournemouth striker turned down a new deal at Meadow Lane after his contract ran out at the end of May, claiming the budget he had been offered at Notts was too small.
After a season of financial turmoil at Portsmouth the club's future appeared to be placed on steadier ground on Thursday after creditors backed a deal which should see the club exit administration this summer.
The administrators will repay creditors at least 20p in the pound over five years. The south-coast club's unsecured creditors are owed a total of £105m.
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