Winger Piteu Crouz joins from Belper Town, midfielder Luke Dean arrives from Scarborough Athletic and full-back Ben Gordon signs from Gainsborough.
Returning to the club is Luke Hinsley, who left the Gladiators for Frickley Athletic earlier this year.
Kittrick said: “I’ve had good chats with all four of the lads and they all want to come here and do well, they’re hungry and some feel they have a point to prove. They’re good football players who want to progress.
“Luke Hinsley contacted me saying he would like to come back. I’ve known of him previously from his time at Frickley and he wants to try again at Matlock. He’s honest, hard working and gets his share of goals so we feel that it’s worth giving him that opportunity.”
Crouz was young player of the year in the EVO-STIK League East Division last season, while Dean played under Kittrick at Scarborough.
Meanwhile, defender Dwayne Wiley and striker Marcus Marshall are believed to have agreed terms to stay with the club.
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