The Ecuador striker joined the London club from Pachuca for a reported £12 million fee last month after scoring three goals for his country at the World Cup.
Valencia was the subject of widespread interest following his exertions in Brazil, but was won over by West Ham's European ambition.
West Ham finished 13th last season after pulling away from a relegation fight and Valencia is aiming higher in his first season in English football.
"Before signing we spoke a lot about that, the ambitions of the club to try to play European football," Valencia said.
"I'm going to work very hard for it and they're going to try to make top four.
"After the World Cup several offers came around but when I found out that West Ham were interested I said definitely yes because it is one of my dreams to play in the Premier League.
"I spoke to [Ecuador captain and Manchester United winger] Antonio Valencia and he gave me some good advice to take this opportunity.
"I hope that I can bring a lot of happiness to the West Ham fans. If we can achieve any European football then that would be fantastic for everyone."
Valencia, who signed a five-year contract with the Upton Park club, is lacking fitness after his extended break following the World Cup and is expected to miss West Ham's Premier League opener against Tottenham a week on Saturday.
But Valencia revealed that he should be available for selection in the near future.
"I'm training normally now and trying to adapt to what the manager wants and the philosophy of the club," he added. "I'm expecting to be ready in between one or two weeks."
