Muntari, 22, is manager Harry Redknapp's third new recruit in a week having signed centre-backs Sylvain Distin from Manchester City and Hermann Hreidarsson from Charlton on free transfers.
The Ghana midfielder has signed a five-year deal at Fratton Park and Redknapp said: "We tried to sign Sulley in the last two transfer windows but Udinese did not want to sell.
"I saw him for the first time in the World Cup last summer for Ghana against Brazil when he was the best player on the pitch.
"And he was outstanding in the matches I've watched him ever since. He will add pace, strength and goalscoring ability to our midfield."
Portsmouth announced the signing on their official website and said the transfer was "for an undisclosed fee".
However, £7million has been the figure popularly quoted in negotiations and will easily surpass the £4.4million they paid French club Auxerre for Zimbabwe striker Benjani Mwaruwari in January last year.
Muntari said: "Portsmouth is a fantastic club with class players like Pedro Mendes, Sol Campbell, David James and Kanu.
"They also have a great manager and great man in Harry Redknapp.
"I have been a Pompey supporter ever since I heard they first wanted me a year ago and watched as many of their games as I could."
Muntari played in a charity match at Portsmouth organised by striker Kanu the day after the FA Cup final and said: "The fans are great and they really love their football here.
"I'm really looking forward to playing in front of them and helping the club make a push for European competition."
Muntari was key figure in the Ghana Under-20 side when just 16 and was a member of the 2001 team which finished runners-up in FIFA's World Youth Championship that year.
The following season he signed for Udinese and spent a year in the reserves before making his first-team debut against AC Milan at the San Siro.
Since then he has made more than 100 appearances for the Serie A side.
His compatriot, Chelsea star Michael Essien, recommended Muntari's signing and said last week: "He will be a really big player in English football."
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