The News of the World says Cameroon star Eto'o, 28, is expected to travel to Manchester in the next few days to finalise the deal. Argentine Tevez will sign a four-year deal worth around £140,000 a week on Wednesday.
Eto'o, who initially demanded £200,000 a week after tax, will put pen to paper on a five-year deal worth £180k a week after tax, with further bonuses tied to success.
A source said: "The player could have earned similar money at Barca. But Eto'o and his people think City could be going places and is excited by the type of players they are attracting."