The Portuguese coach replaced Louis van Gaal last month after United finished fifth in the Premier League to miss out on Champions League football for the second time in three seasons.
De Gea said: “I think United needed a coach like him – a winning coach with personality.
“United’s decision to sign Mourinho is the right move.”
He added: “I arrived at United to win titles; it’s true that in the past two years we haven’t been at the level that this club deserves, but we hope that with the coaching change, we can return United to the top.”
Mourinho won three Premier League titles in two spells at Chelsea and also won league titles at Porto, Inter Milan and Real Madrid as well as the Champions League with Inter.
De Gea came close to joining Real Madrid last summer, but the Spaniard says he is happy at Old Trafford now.
“I have three years left at Manchester, a club that has given me everything,” the 25-year-old said.
“This is a very big club, that gives me a lot of affection each day. I’m very grateful to United, I’m very happy there.”
