The former Cameroon international has signed a two-and-a-half-year deal with the Serie A club, bringing an end to his short stay at Everton.
Since taking over last year, owner Massimo Ferrero has regularly spoken of his desire to see Samp gain a place in the Champions League and Eto'o feels it is an achievable target.
"I've shown that by working hard and following my dream you can do anything," the 33-year-old, whose new side sit fifth in the league, said.
"I became one of the top players in the world. So the president has every right to dream and to achieve his dream."
Eto'o was cagey when asked about the apparent decline of the Italian top flight, however and said he would rather concentrate on Sampdoria's progress rather than the wider situation in Italian football.
"Several years ago I was asked the same question when I arrived at Inter," he added. "It was a period when a lot of big players were leaving Italy.
"Back then we had Kaka, Zlatan Ibrahimovic and Andriy Shevchenko. Now, a lot of them have moved on but football is all about what happens on the pitch.
"I proved that by winning everything with Inter. I hope to keep Sampdoria winning, I don't want to hear talk of a crisis."
