Casey, 18, has decided to leave the Scottish champions after failing to make the breakthrough at Parkhead and he has signed a three-year deal at Fratton Park.
The Glasgow-born ace is highly-rated and he will add competition for places in Pompey's midfield for the forthcoming season.
Mapeza, who is out-of-contract at Austrian outfit SV Ried, is set to fly into England this week to seal a deal.
The 29-year-old should have joined Pompey last year, but red tape killed the move, but he now qualifies for a work permit as Zimbabwe have climbed to 67 in the Fifa world rankings, which makes him eligible.
Meanwhile, one player who is on his way out of Fratton Park is midfielder Carl Pettefer, who is joining Bournemouth on loan.
Pompey boss Graham Rix feels the move will be good for the player as it will get him first team football, which he would not be guaranteed at Fratton Park.
"It would be great if he could get away and play 25 games for Bournemouth," said Rix. "He's got ability, and I like his attitude.
"He's got a chance of making it and going on loan will do him the world of good."
