Gracia, who was born in Pamplona where Osasuna are based and has coached Spanish teams including Villarreal B, Pontevedra, Cadiz and Almeria, has signed a two-year contract, his new club said on their website.
"I have found a dressing-room that is determined to do things well, with the values of honesty and identity above all else," the 43-year-old said at his presentation on Thursday.
"We need the players to recover physically and also give them a psychological lift," he added.
"We have to get the most out of them to create a more competitive team and we also have to look at why they have not scored goals and why they have let in so many."
Osasuna finished seventh in the 2011-12 season under Mendilibar but after a dramatic slump in form narrowly avoided relegation last term.
They lost 3-0 at home to Villarreal on Saturday and are bottom of the standings after three matches with no points having conceded seven goals and scored just one.