Kittrick has taken the reins at Matlock Town.
He will be joined by his former assistant-manager at Boro Chris Bolder.
The pair left Boro after the defeat at home to Stalybridge and have since been replaced by John Deacey.
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.”