Barker, who left Crawley last month after 16 months in charge, has signed a rolling contract at Fratton Park.
Pompey is the third managerial post for Barker, who took Bury out of League Two in 2011 and steered Crawley to 10th in League One last season.
And he told Sky Sports News: "I'm excited. Just look around the place and imagine it with 15,000 or 16,000 people in it. That can't do anything else but make you excited.
"It's my third job in a short spell, and I'm looking forward to seeing where we can take this football club. We need to build on the passion and the pride of the supporters and try to give them something to shout about."
Coppell, who worked with Barker at Crawley, will work for no salary at Portsmouth.
And Barker said: "It's a tremendous help for me as a manager who's still learning. He's got a massive amount of experience as a player and manager, and hopefully he'll help everybody at the football club.
"It won't be just geared around me. He'll be an advisor to the board and to anyone else that needs his opinion - to the staff, the players."
Barker inherits a side 17th in League Two. He said: "Initially the target is to get out of the bottom half, and as soon as we get into the top half the closer we are to getting into League One.
"The thing that intrigues you about here is that there's no glass celing. This club can go as far as it wants to, and the supporters want to. We'll keep working until we get it back to where it's been before.
"Many different people own football clubs, but for this club to be run by a large proportion of supporters makes it a special place. hopefully that will create a special bond between supporters and everyone who works here."
Coppell, who worked with Barker at Crawley, told the club website: "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."