The Spanish left-back joined the Blues from Italian club Fiorentina for around £23million on deadline day and admitted it was not a tough decision to make the move to Stamford Bridge.
"I am very happy to be here and to be back in the Premier League," Alonso told Chelsea TV.
"It is a big decision, a big step in my career.
"I'm more ready than before and this is a very big thing. I think it's time to win trophies now and give my best to help the team.
"We have to fight for every competition. We have top players, we're a top club so we're going to try and win every competition we play."