Odegaard has joined Arsenal until the summer after moving to them on loan from Real Madrid earlier this week.
The Norwegian comes with a big reputation, having been tipped for the top ever since he was 15, but Leno is backing him to shine at Arsenal.
“I think we should all be very excited because he is an attacking midfield player who is turning, wants to go forward, wants to play passes and create chances and have assists,” said Leno.
“In his first days he has been very impressive and has been very open to everyone, and I think we will have a lot of fun with him in the next months.”
Arsenal’s draw with Manchester United on Saturday extended their unbeaten run in the Premier League to seven games.
In that time they’ve conceded just two goals and kept five clean sheets.
When asked what the key to the turnaround in defence has been, Leno said: “I think our mentality.
“Because everybody is defending, even the striker is sometimes defending in the box and then you can see the difference.
“It is much harder to score goals against us and even to create clear chances.
“For me, of course as a goalkeeper, it is always better to have a clean sheet but I think to be a successful team the defence is the most important thing.”