The former Wolves ace has taken Marcus Rashford's No10 shirt and arrives as the club's senior striker.
“I really think the pressure at this club is not really pressure it's a privilege, because this is one of the biggest clubs in the world,” said Cunha from United's New Jersey preseason base.
“When Ruben (Amorim, manager) comes to me and shows all the pressure that I have to help put the club back in the perfect times again, I feel like it's a challenge that I want to do for me and my career.
“United is always one of the clubs that needs to be there and to be someone who can be a part of the process is something that, like I say, is a big privilege.
“So I don't think about being perfect at the start, honestly. I think to be myself and to help the team. I have started to feel that I'm part of the group, we start to do everything very well and then start thinking about doing everything well.
“So I'm very comfortable to be here, I'm very comfortable with the pressure right now, and I hope everything can be better too - don't think about the bad times.”
Asked why he chose United, Cunha said: “United was always my dream club and when you can make a dream come true, it's an easy decision to make."