The 21-year-old completed a £9m switch from Wigan Athletic to the Blues last week after months of speculation.
The Nigerian has been handed the number 13 shirt at Stamford Bridge and is now eager to make his first appearance for the Londoners.
"Following the successful conclusion of my transfer to Chelsea I'm now looking forward to getting started with my new team mates and can't wait to make my debut," Moses said in a statement.
"I'm very ambitious and to be joining a club with the history of Chelsea, the current European champions, is a dream come true for me. The team have had a great start to the new season and I'm looking forward to playing my part in continuing our good form in the coming weeks and months.
"I'm now really excited about the challenges ahead at Chelsea and look forward to a long and successful career at Stamford Bridge."
Moses has three international caps for Nigeria.