Norris had turned down the offer a new two-year deal at Portman Road.
Pompey boss Steve Cotterill told BBC Radio Solent: "David has stayed patient while we waited for the takeover, and I'm delighted to have finally got him."
"We missed out on three or four free transfers while we waited for the takeover to be finalised, but David really wanted to come here."
Norris, who scored 11 goals last season, cost Ipswich ?2m when they bought him from Plymouth in January 2008.
"He brings good leadership qualities. He's been captain of Ipswich, which is a fantastic club, and he also brings goals with him. He's a top lad and we're really looking forward to working with him."
Cotterill has found himself unable to add any permanent signings in recent months, due to the ongoing uncertainty over the club's off-field future.
"It's just nice to sign a player", Cotterill added.
"It's been unbelievably difficult over the last 12 months, so to sign a player of David's quality is a real bonus. I'm sure he'll go down well with the Pompey fans."
Source: BBC Sport
Source: BBC Sport