Costa has joined the Blues from Atletico Madrid for £32m, and after seeing his forward net twice against Real Sociedad on Tuesday evening, Mourinho has insisted that the club have paid under the odds for the Spanish international.
The 51-year-old told the club's official website: "Diego is a team player who works hard, he's not just about goals. It's about his defensive work, mentality and ambition. This is the player that we bought and we were waiting for since last season. This is why we didn't buy a striker in the winter market. We were waiting for him, we have him and hopefully everything goes well.
"He looks adapted to the team, and the Premier League, not just Chelsea, should be happy. Sometimes we lose important players going to other countries and sometimes we bring new top players here.
"You can consider that [a bargain] because the market is crazy and the values are very high. For a striker like him, a champion in Spain, a Champions League finalist, a 25-year-old, we consider that the price was very much in our favour."
Chelsea start their Premier League campaign with a trip to Burnley on Monday evening.