The 22-year-old, who recently served a prison sentence for drink-driving offences, agreed a three-year contract and the club have an option to retain the winger for an extra year.
Pennant has been on loan at St Andrews since January after finding his first-team opportunities limited at Highbury.
A statement on the club's official website confirmed the deal, and added: "The club also has a further one-year option on Pennant."
Steve Bruce has been expected to sign the former England Under-21 winger after supporting the player through his prison sentence.
Pennant admitted earlier in the season he was unsure of his future at Highbury after seeing a number of foreign youngsters push ahead of him into the first team.
"I've been here for seven years and the amount of games I've played is poor, I don't know if it because I'm English," Pennant said last month.
"I scored a hat-trick on my first (Premiership) start, it was the last game of the season and after that I was shipped off to Leeds for the season.
"It was frustrating but I did well there, came back, and it still did not make a difference."
Pennant arrived at Highbury in 1999 for £2million from Notts County, but he never fulfilled his billing as a teenage prodigy.
He did score a hat-trick on his first Premiership start, in a 6-1 rout of Southampton, but failed to establish himself in the first team.
After loan spells at Watford and Leeds he was back at Highbury, but again was not in manager Arsene Wenger's plans.
Pennant was convicted of drink driving offences last season and received a three-month prison sentence when he offended again, in January.
Bruce had already taken him on loan and the winger played just days after being released on parole, serving 30 days of his sentence.
Although Bruce has been criticised for showing faith in Pennant, the player is grateful for the backing of his boss and Blues fans.
"The support I've got from our fans has been magnificent. Since I came to the club, went inside and came out, they've stuck by me 100% and I have to say thank you to them," he said recently.
"Steve Bruce, a great manager, has had my back since I've been at the club which is great as well."
