Luton have made their ninth summer signing following the arrival of winger Danny Green.
Notts County have signed Togo international Mawouna Amevor on a two-year deal.
Jose Mourinho hinted Chelsea had given up their pursuit of Manchester United striker Wayne Rooney after two rejected bids and now has turned to Eto'o.
Mourinho and the Cameroon striker are to be reunited after working together at Inter Milan, with Chelsea and Russian club Anzhi Makhachkala having agreed a deal.
Eto'o said on chelseafc.com: "I am very happy to be here but also anxious because I want to get playing as soon as possible.
"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."
Capturing Eto'o, who commanded wages reported to be in the region of £300,000 a week in Russia, is at odds with Chelsea's recent transfer policy of signing younger players.
Samuel Eto'o factfile
Samuel Eto'o factfile
1981: Born Samuel Eto'o Fils on March 10 in Douala, Cameroon.
1997: Makes his international debut for Cameroon in a 5-0 friendly loss to Costa Rica. Signs contract with Real Madrid, but is loaned out to Leganes.
1998: June - Included in Cameroon's World Cup squad aged 17 years and three months. Becomes the youngest player to feature at France 98, during a 3-0 group-stage loss to Italy.
1998: July - Loaned by Madrid to Real Mallorca.
2000: February - Wins African Nations Cup as Cameroon beat Nigeria in a penalty shoot-out.
July - Makes move to Mallorca permanent.
September - Scores from open play and adds a penalty in the shoot-out of the 2000 Olympic Games final as Cameroon beat Spain to take the gold medal.
2002: Helps Cameroon lift the African Nations Cup for a fourth time after penalty shoot-out win against Senegal.
2003: May - Scores two late goals in the Copa del Rey final to help Mallorca beat Recreativo de Huelva.
2004: July - Signs for Barcelona for around £21million.
2005: May - Scores 25 goals in 37 league appearances to help Barcelona win Primera Division.
December - Finishes third in FIFA World Player of the Year voting.
2006: May - Collects another Primera Division title and finishes as league's top scorer with 26 goals. Scores equaliser as Barcelona come from goal down to beat Arsenal 2-1 in Champions League final in Paris.
2007: February - Refuses to come on as substitute for Barcelona in a league match against Racing Santander.
October - Receives Spanish citizenship.
2009: May - Helps Barcelona achieve league, cup and Champions League treble. Scores 30 league goals and nets as Barcelona defeat Manchester United 2-0 in Rome to land their European title.
July 27 - Signs five-year deal with Inter Milan, as part of exchange move involving Zlatan Ibrahimovic.
2010: March 17 - Scores as Inter win 1-0 at Chelsea to complete aggregate 3-1 success in Champions League second round.
May - Helps Inter win the Champions League, Serie A and Coppa Italia - for Eto'o a second successive treble-winning season.
2011: May - Ends the season with 37 goals for Inter, but the club miss out on Champions League and Serie A silverware. Inter retain Coppa Italia as Eto'o scores twice in 3-1 win over Palermo in the final.
August - Joins big-spending Russian club Anzhi Makhachkala, reputedly on a world-record salary for a footballer worth an annual £17million after tax.
2013: August 29 - After Anzhi rein in their spending, Eto'o is allowed to join Chelsea on a one-year contract.