After 16 months at Crawley, who he steered to a 10th-place finish in League One last season,Barker 38, signed a rolling contract at Fratton Park.
Pompey is his third managerial post having started at Bury in April 2011 with eight games remaining, winning six of those to secure promotion from League Two.
His playing career saw him spend time at Sheffield Wednesday, Linfield, Brighton, Macclesfield, Rotherham, Mansfield and Hartlepool.
“This is a fantastic opportunity for me,” Barker told Portsmouth’s official website. “I’m very excited to be at this club with its great history.
“Richie asked if I’d like to be involved and I jumped at the opportunity.”
“Everyone knows how passionate the people of Portsmouth are about their football club.”
Coppell, who worked with Barker at Crawley, added: “It’s a new challenge for me and I’m very excited. Richie asked if I’d like to be involved and I jumped at the opportunity.”
Pompey chief executive Mark Catlin said: “I think the board have made a great appointment. The combination of Richie and Steve is just what the club needs at this time.”