The three-time Champions League winner, who was released by Chelsea at the end of last season, joined Everton on a two-year contract after being linked with several other clubs.
The 33-year-old's single campaign at Stamford Bridge was best remembered for unguarded and unflattering comments by Mourinho about his age.
The veteran striker later made known his frustration about those remarks, labelling Mourinho a "fool", but he now seems keen to consign the controversy to history.
Eto'o said on Wednesday: "The only thing I have to say vis-a-vis Jose Mourinho is to thank him.
"It is down to Jose Mourinho that I had the opportunity to be accepted and integrated into the Premier League, to play some great matches
That is the end of the discussion."
Eto'o's signing this week raises the possibility of a potential Everton debut against his old club, with Chelsea visiting Goodison Park in the Barclays Premier League on Saturday.
The former Barcelona and Inter Milan forward said: "I am not concerned about that aspect of it - that it is against my ex-team.
"The important thing is to integrate myself into my team-mates' way of working and get myself ready during the training and preparation, potentially, for that match.
"If that is not the case, should I not feature, it is important for me to get my head into the training for each match."
One of the clubs most strongly linked with Eto'o, particularly in the last week, were Merseyside rivals Liverpool, before they eventually completed a deal for Mario Balotelli.
Eto'o, unveiled by Everton at a press conference at their Finch Farm training complex, refused to name which other clubs he had been approached by.
He said: "During my meetings with (Everton manager) Roberto Martinez I had a very good feeling
We had so much in common.
"Everton correspond with my philosophy on football and how the game is.
"In the last 10 days I have travelled quite a lot and spoken to quite a few managers.
"Over the course of those travels the person who I felt the most inspiring and would allow my contribution to best correspond was Roberto Martinez."
Eto'o has been replaced as Cameroon captain following his country's poor World Cup campaign but he was also unwilling to discuss international matters.
"I am an Everton player now and that is the only thing that concerns me," he said
"That is my new challenge."
Martinez will assess the player's fitness before deciding whether he can throw him straight into action against Chelsea, but he admits stopping Eto'o could be difficult.
Martinez said: "We had a conversation
Being realistic I would have loved him to have 10-11 sessions before putting him in a competitive environment but I very quickly learned I was wasting my time.
"He wants to be helpful to the team straight away, he wants to be involved.
"It will come down to what sort of condition he has over the next two or three days."
Martinez is impressed by Eto'o's desire to help Everton push on to the next level having snubbed better financial offers from elsewhere.
The Everton manager said: "It was an instant feeling
Once I met him and we spoke about football, I was so impressed where he was mentally - a real desire and hunger to achieve.
"In every aspect he is perfect for the team and the squad
It is the perfect timing to start an exciting relationship.
"He had many options abroad
It could be a financial decision or a footballing decision, but he wanted to make a footballing decision and he chose us
That is a compliment."
Martinez added that Eto'o's arrival was likely to signal the end of his summer transfer activity.
He also ruled midfielder Steven Pienaar out of Saturday's game with a groin injury but said another former Chelsea striker, Romelu Lukaku, who has a toe problem, was still being assessed.
Source : PA
Source: PA