The 21-year-old Nigeria international joined the Blues from Wigan for a fee in the region of £9m last week after two years with the Latics.
"I'd like to put on record my sincere thanks to everyone at Wigan Athletic for the tremendous support they showed me during my time there," said Moses in a statement.
"I'd like to thank the chairman, Dave Whelan, and all of the staff at Wigan for giving me the chance to play in the Premier League.
"In particular, I'd like to thank the manager, Roberto Martinez, who has been a major influence on my career up to this point, as well as the Wigan fans - who were always great with me."
Moses added that he is keen to prove himself at Chelsea.
"Following the successful conclusion of my transfer to Chelsea I'm now looking forward to getting started with my new teammates and can't wait to make my debut," he said.
"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."
Chelsea, who won the Champions League last season, will take on Europa League winners Atletico Madrid in the UEFA Super Cup on Friday.