The 32-year-old will be officially unveiled on Friday but underwent the formalities of a medical on Thursday morning before agreeing personal terms.
The four-time African Footballer of the Year, who arrived in London on Wednesday night after taking the train from France to St Pancras Station, added: '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.
Parading: Eto'o has signed for Chelsea
Pen to paper: Eto'o signs the contract in the presence of Chelsea club secretary and director David Barnard
Pleased to be here: Eto'o has signed on a free transfer
'I am very happy to be here but also anxious because I want to get playing as soon as possible.'
Jose Mourinho moved for Eto'o after two Chelsea bids for Manchester United's Wayne Rooney were rejected and the Premier League champions declared he was not for sale.
Mourinho is continuing to add to his galaxy of stars though as talks continued on Thursday with Porto's Christian Atsu.
The 23-year-old Ghana international is poised to undergo a medical this morning although the Portuguese side are hoping to agree a sell-on clause in the £3.5million transfer.
Arrival: Eto'o arrived at St Pancras on Wednesday night ahead of putting pen to paper for Chelsea
Seal the deal: Eto'o shakes hands with Pini Zahavi (left picture) and strides towards his car (right)
Whisked away: Eto'o, who is taking a huge pay cut to join Chelsea, leaves St Pancras on Wednesday night
Solution? Samuel Eto'o has sealed his move to Chelsea as Jose Mourinho ends his striker search
Chelsea manager Mourinho was Eto'o's boss at Inter Milan when they won the Champions League in 2010. He became the highest-paid player in the world when he moved to Anzhi in 2011 on an estimated £350,000 a week.
However, he took a £10m pay cut to come to Chelsea sweetened by a pay-off from the Russian club who also sold Chelsea their Brazilian attacking midfielder Willian, 25.
Meanwhile, former Queens Park Rangers defender Christopher Samba, who was linked with West Ham and Tottenham this summer, was among the latest players to leave Anzhi when he, Alexei Ionov and Vladimir Gabulov joined rivals Dinamo Moscow on Thursday.
Former Barca striker Eto'o did not travel to Prague for Friday night's European Super Cup clash with Bayern Munich - neither did Willian, whose move from Anzhi was confirmed on Wednesday - but he added: '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 and see if I can have the same success as in my previous clubs.
'I don't see it as a final challenge, but to have a good time, enjoy my football, and have success with this team.
Target: Mourinho didn't select any strikers at Old Trafford and the chase for Wayne Rooney seems to be over
'I've had a couple of opportunities to come to England before, including the first time Jose was here, but it didn't work out for one reason or another.'
The move might never have happened if Mourinho had received the indication from Rooney that he wanted to join Chelsea.
Speaking prior to confirmation of Eto'o's arrival, Mourinho appeared to have conceded defeat in the bid to capture England striker Rooney, who played for United against Chelsea on Monday and afterwards praised the 'fantastic' reception he received at Old Trafford.
Mourinho said: '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.'
Capturing Eto'o is at odds with Chelsea's recent transfer policy of signing younger players. It also leaves a question mark over the futures of Demba Ba and Fernando Torres as Mourinho has made it clear four strikers is too many and that Romelu Lukaku is key for Chelsea's future.
Ba's place in the squad seems most at risk, but Torres has still to repay the £50million fee paid to Liverpool, as Mourinho admitted earlier this week.
Reunion: Eto'o and Mourinho won the treble at Inter Milan in 2010
Eto'o became Chelsea's fifth signing of the summer transfer window, following Andre Schurrle, Marco van Ginkel, Mark Schwarzer and Willian, who can be expected to provide the ammunition for the striker to score.
'I think Willian he is one of the best players in modern football,' Eto'o said.
The 32-year-old Eto'o began his career with Real Madrid before, following a spell with Real Mallorca, surging to prominence with Barcelona, scoring 152 goals in 232 appearances for the Catalan club.
He has a controversial history with Chelsea.
Following a bad-tempered Champions League encounter at Stamford Bridge, the striker criticised Mourinho, referee Pierluigi Collina and made a claim in the Spanish media that he was called a monkey by a Chelsea security guard. The allegations were swiftly denied by Chelsea.
All smiles: Brazilian playmaker Willian revealed his delight at completing his move to Stamford Bridge
Eto'o, who also played at Stamford Bridge with Inter, added: 'They were always games between two big clubs. They didn't always finish well, but the most important thing is they were spectacular games every time.'
The striker netted 53 goals in 102 appearances for Inter before joining Anzhi in August 2011.
