The Cameroon striker, who played under Mourinho at Inter Milan, has left the Russian club Anzhi Makhachkala to sign a one-year deal at Stamford Bridge.
Eto'o is apparently 'Plan B' after Manchester United rejected two Chelsea bids for Rooney, with Mourinho opting against lodging a third, having said he had back-up options.
The former Barcelona striker did not travel to Prague for Friday night's European Super Cup match with Bayern Munich - neither did Willian, whose move from Anzhi was confirmed on Wednesday - but is eager to progress his career.
"I am very happy to be here but also anxious because I want to get playing as soon as possible," said Eto'o. "It wasn't a hard decision. I saw the qualities Chelsea have, and I was very happy with Jose Mourinho before, so when the opportunity came, I was very happy to take it. I have had a career where I have been lucky enough to win a lot of trophies in different countries, but one of my last dreams as a professional is to come and play in England."