Torres endured a mixed three-and-a-half-year stint at Stamford Bridge following a £50m move from Liverpool, and the 30-year-old says that Costa's arrival made his decision to leave that bit easier.
"I had decided to leave Chelsea," he told Corriere dello Sport. "With Mourinho there was a relationship of respect, but the club had bought a new striker.
"With the coach I had spoken often about my future. He wanted me to stay in London, but I needed a new stimulus for my career.
"That day I received a phone call from Milan. I was presented with the offer I had been waiting for. I was at a particular moment in my career."
Torres netted 45 goals in all competitions for Chelsea.