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."
Azpilicueta, who is uncapped by Spain, started his career at Osasuna before leaving La Liga for Marseille in 2010.
He becomes the fourth Spanish player at Chelsea, linking up with Juan Mata, Oriol Romeu and Fernando Torres.
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.
The Nigerian international played for Crystal Palace before joining Wigan in January 2010.
Moses made his debut for Nigeria against Rwanda in February.
Di Matteo has made six major signings since Chelsea won the Champions League in May - Eden Hazard, Oscar, Marko Marin, Thorgan Hazard, Azpilicueta and Moses.
