The 21-year-old had been the subject of prolonged speculation over the summer with reports constantly linking the winger with a transfer to west London, a deal that was officially completed on Friday.
The Nigerian admits the Blues' interest shocked him at first, but says he was delighted to make the switch to the reigning European champions, something he believes any player would have done.
"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," he told the club's official website.
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"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."
Roman Abramovich has dug deep into his pockets this summer in a bid to avoid a repeat of a disappointing sixth-placed finish in the Premier League table last year, only qualifying for the Champions League as eventual winners.
Eden Hazard, Oscar, Marko Marin & Cesar Azpilicueta are among the names already brought in, as well as Moses, and the spending has paid off so far with Roberto Di Matteo's men sitting pretty on top of the table with three wins from their first three matches.
The former Wigan attacker says he is looking forward to working with some of the best players on the planet, while insisting he will do his best to add to the team in their hunt for titles.
"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 added.
"The club has done well for the past few years, they have achieved a lot, and I am delighted to be able to play with these world-class players.
"I just want to ask the fans to sit tight, there is more to come from Victor Moses and I hope to do my best for the club and that there are more trophies to come in the future."