The 21-year-old joined the Blues from Wigan for an undisclosed fee on Friday following a protracted period of speculation, and was paraded before the club's supporters prior to their 2-0 win over Newcastle on Saturday.
Moses is in line to make his debut in Friday's night's Super Cup encounter against Europa League winners Atletico Madrid, and the former Crystal Palace youngster cannot wait to get started.
"When I first heard that Chelsea had come in for me I was surprised, but I had a call from my agent saying they were really interested in me and what did I think," Moses told the official Chelsea website.
"I said they are the European champions and anyone would like to play there and now that everything is sorted, I am delighted to be here.
"I am happy to come back to London as I grew up here and it is a great honour to play for the club that won the Champions League."
With the likes of Eden Hazard, Oscar and Juan Mata already giving manager Roberto Di Matteo plenty of creative options going forward, Moses could find first-team opportunities hard to come by, but he insists he is unfazed by the competition.
"There are a lot of world-class players here and I am here to do my best for the team and to help them win more trophies," he said,
"The club has done well for the past few years, they have achieved a lot, and [it is great] for me to be able to play with these world-class players."
Moses emerged from Palace's academy to make his first-team debut in 2007, before joining Wigan in 2010, where he went on to make 74 league appearances, scoring eight goals.
Moses' versatility was a feature of his time at Wigan, and he expects Di Matteo will also look to exploit those qualities as the club bids for success on several fronts.
"I went to Wigan to play left wing mainly but then the manager saw the way I was playing and he mostly used me on the right. Last season I played more on the right but sometimes on the left," he said.
"I can also play up front or behind the striker, I can play anywhere up front.
"I'm comfortable wherever the manager wants to play me."