The 32-year-old is the second player to arrive at Chelsea from Russian club Anzhi Makhachkala following the acquisition of Willian on Wednesday.
Having failed in two bids for Manchester United's Wayne Rooney, Chelsea were desperate to bolster their attacking options and moved quickly amid reports that Eto'o was considering a return to Inter Milan.
"I am very happy to be here but also anxious because I want to get playing as soon as possible," Eto'o told Chelsea club website.
"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."
Four-time African Footballer of the Year Eto'o was an integral part of Mourinho's Champions League-winning Inter side in 2010, before heading to Anzhi the following year to become the highest-paid player in the world.
Anzhi are in the process of slashing their wage bill with owner Suleyman Kerimov desperate to balance the books of the financially-troubled club.
On the international stage, Eto'o has been a regular for Cameroon after making his debut before he turned 15. At the age of 17 he was the youngest player at the 1998 World Cup in France.
Four years later he scored the winning goal as Cameroon bagged their only victory of the 2002 World Cup by beating Saudi Arabia.
Eto'o is the leading goalscorer in the Africa Cup of Nations and was also part of the Cameroon team which won gold at the 2000 Olympics in Sydney. He also captained Cameroon at the 2010 World Cup in South Africa.
Mourinho moved to bring in Eto'o after appearing to have conceded defeat in the bid to capture Rooney from United.
Rooney played for United against Chelsea on Monday night and Mourinho is not planning a third bid after seeing two offers rejected earlier in the transfer window.
"Rooney," said Mourinho at a press conference on Thursday. "I told you what I have to say. I think I (made it) very, very clear that we didn't start the process (a third bid).
"We have nothing more to say. He's a Man United player and no more than that."