The 31-year-old has joined on a season-long loan from League One Port Vale.
He will provide competition to Scott Loach for the number one spot.
Covolan said: “When I spoke with my agent and I got the opportunity to come here I knew it was the right decision. With what the club wants to achieve, it felt right.
“I’m absolutely buzzing to be here, I think we’re going to make a good go of it this season.
“I want to fight for the position and fight for promotion back to the Football League.
“The gaffer has asked me to make match-winning saves and that’s what I want to do. I want to achieve what everyone at Chesterfield wants.”
Covolan joined Vale in June 2021 and has gone on to make 22 appearances, recording seven clean sheets.