The 24-year-old signed for the Hammers on Thursday, after leaving Ipswich for an undisclosed fee, and is currently training in France with his new team-mates.
The former Tranmere Rovers defender spoke of his delight at finally securing an opportunity to play in the Premier League.
"I'm very excited to have signed here," he told West Ham's official website.
"It's a massive club and I can't wait to get ready for the season ahead.
"When I knew West Ham were interested it was an easy decision to make! Everyone knows it's a massive club and a couple of years down the line they'll have the new stadium too.”
Cresswell, who was born in Liverpool in 1989, made his debut for Tranmere aged 18 and has risen through the ranks of the Football League.
"It's everyone's ambition to play in the Premier League, and to play in front of 35,000 week in, week out, is a dream come true for me,” he said.
"I know we've got Spurs, Man City and Liverpool at home early on and there's no such thing as an easy game in the Premier League, but I'm going to relish every one and hopefully I can play a big part in it.
"If you ask any player in the Football League, they want to play in the Premier League. Some people have to gradually go through the leagues and fortunately for me that's the way it's worked out so I can't wait to get going.”
Cresswell has no new-kid nerves about his team-mates, and is looking forward to working with skipper Kevin Nolan.
He sees the training camp in France as the ideal opportunity to get to know the team.
"Not really knowing anyone, apart from Stephen Henderson who was on loan at Ipswich, being away in France for my first week at the club is a good chance to mingle and get to know the lads," he said.
"Being a fellow Scouser, I think Kevin Nolan is the only one who is going to be able to understand me! I just can't wait to get to know everyone and hopefully settle in as quick as possible."
West Ham kick off their 2014/15 campaign in a hotly-anticipated London derby on Saturday August 16, facing Tottenham Hotspur at home.