The Mexico international is back in the Premier League after a three-year absence, in which time he has taken in spells with Real Madrid and Bayer Leverkusen.
Hernandez, who completed his move to West Ham on Monday night for a fee of £16m, is looking forward to playing at Old Trafford after scoring 59 goals in 157 appearances for United during his previous spell in English football.
"I think I will be a little bit more excited than my teammates to be back at Old Trafford," Sky Sports News quotes him as saying. "To start the season with my new team there is important and I will be happy to be there. I was desperate to come back to the best league in the world.
"It will help me a lot to improve as a player and person. We want to fight to aim for the Europa competitions. Slaven Bilic was a massive part of why I joined. Since I joined Bayer Leverkusen he wanted me, he spoke with me. He did everything he could to bring me here but couldn't for a lot of reasons and now I am here I want to repay him.
"My aim is to give my best, to try to give back all the confidence and support from my manager and the board, and help my team get as far as we can this season. You can see in this window they've spent very well on good players because we want to be better compared to the last season."
Hernandez scored 39 times in 76 appearances for Leverkusen, though he has found the net in just five of his last 31 outings for club and country.