Eto'o, 32, joins the Blues on a one-year deal after spending two seasons at the Dagestan-based club.
"I am very happy to be here but also anxious because I want to get playing as soon as possible," the Cameroon striker said.
"'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."
The signing of the Cameroon international, who won the Champions League with Mourinho while at Inter Milan, would appear to end Chelsea's interest in Wayne Rooney, who the West London club have been courting all summer.
Eto'o, who has also played for Barcelona, Real Madrid and Mallorca, surprisingly joined big-spending Anzhi in 2011 on a reported world record wage.
But he has fallen victim to the club's cost-cutting measures, which also saw Brazil playmaker Willian move to Stamford Bridge this week.
The move is unsurprising due to Mourinho's previous success with the player, and the relationship between the respective clubs' Russian owners.
Eto'o scored 25 goals in 53 Russian Premier League matches for Anzhi and is best known for his spell at Barca, where he scored more than 100 Liga goals and won three Liga titles and two of his three Champions Leagues.