No fees were disclosed by the Londoners but media reports said Spaniard Azpilicueta, 22, cost about seven million pounds while Moses was bought for nine million pounds.
"I'm a right-back and my first mission is to defend for the team but I also like to offer solutions offensively and I enjoy going forward," the former Marseille player told the club website.
"I have watched a lot of Premier League football on television. It will be difficult at first but I hope, given time, I will be able to play well and adapt."
Moses, 21, joins the Stamford Bridge team after having impressed manager Roberto Di Matteo with his performance in Wigan's 2-0 league defeat at Chelsea's hands on Sunday.
"He caught the eye with his strong running," the European champions said on their website.
