The 39-year-old former Stoke, Sunderland and Republic of Ireland midfielder, confirmed as the club's new boss on Monday following the sacking of Greg Abbott last month, has been given a contract which expires in June 2015.
Kavanagh, who has been with the Cumbrians as player, player-coach and assistant manager since 2009, has steered the club from third-bottom up to 14th place in the table following three straight wins during his spell as caretaker-boss.
"I think there are feelings of excitement, a challenge, a little bit of everything at the moment," Kavanagh told the club's official website.
"There's a huge amount of pride as well because a lot of work has gone into the last three weeks and everyone has got right behind it.
"That's hugely satisfying and I'm really thankful for it. It's been a real team effort, we've juggled the balls and got the results we wanted to get, but we are under no illusions that the real hard work starts now."
Kavanagh will work with assistant manager and former academy boss David Irons and first-team coach Tony Caig.
"It's a huge opportunity for me, that goes without saying," Kavanagh said. "Because of the way I am, and the way I've always been, I don't want to fail or to be associated with failure.
"I put a huge amount of pressure on myself and I know where I want to get to.
"I'm going to give my all for this club because I want it to be successful.
"It isn't about money, or anything like that, it's about the three of us being given an opportunity to become a successful management team."
He added: "I really want this and I'm desperate for everything to be right at this club.
"I want the players to improve and to achieve everything they can - because they deserve it.
"We will disappoint a few players along the way because they won't be playing games, but it's hugely important that everyone is behind what we're trying to do."