Kittrick, 61, replaces Dave Frecklington who left the Proctor Cars Stadium after the Gladiators’ final day defeat at Stafford.
He left the Seadogs back in March after they fell out of the play-off places.
Kittrick said: “It's an honour to be the manager. Matlock is a well established non-league club who’ve underachieved on the pitch during the last two or three years.
“We’re wanting a team hungry to win things, they’ll be fit and play entertaining football. All of the teams I’ve managed have played good football.
“I’ll be chatting to the players and see where we are. I understand that the club has a really good academy, my belief is that if they’re good enough, they’re old enough.
“I have plenty of targets, it’s a funny time of the year at the moment with players going for who pays the biggest money.
“We’ll be fishing in a different pond for our players but we aim to get a really good side together to entertain the fans.
“Chris (Bolder) and I haven’t come to make the numbers up, we want to win something. Off the pitch everything’s right, people are working really hard, now we want success on the pitch.”
Kittrick won the Northern Premier League with Guiseley in 2010 and also led Scarborough to promotion in 2017/18.
His former clubs include Ossett Town and AFC Telford. He will be joined by Chris Bolder, who was with him at Scarborough and has had previous managerial experience at North Ferriby United.
Chairman Tom Wright said: “We had 40 applications and some very good ones at that and we’d like to thank everyone who has applied but we felt that Steve was the outstanding candidate to take this club forward.
“His CV is impressive and we now ask all our fans to get behind him, Chris and his team.”