The Blues confirmed on Tuesday that they had agreed to pay the prolific striker's buyout clause of £32m.
The 25-year-old will join Jose Mourinho's side at Stamford Bridge after scoring 27 goals in 35 games in La Liga, which helped guide Atletico to the league title last season.
"He's at an age where he can continue to improve, so let's hope he can develop further," Simeone told Goal.com.
"He'll have to adapt quickly to the system at Chelsea and to the coach, but let's hope the team can take full advantage of his characteristics. I see a player very much on the way up and I'm sure he'll be a success."
Costa failed to impress during Spain's failed World Cup campaign in Brazil, where they were unable to progress past the group phase.