The 40-year-old Australia goalkeeper became Jose Mourinho's third summer signing, three years after a move to Arsenal failed to materialise.
Schwarzer, who has spent 15 years in England with Bradford, Middlesbrough and the Cottagers, said: "When I moved to Fulham, I thought that was it and then the Arsenal thing popped up so after that experience I said 'Never say never'.
"It's proven to be true. I still say 'Never say never'. It's not over until it's over."
Schwarzer will be 41 in October, but has the 2014 World Cup in his sights and believes he is playing as well as ever.
"I am 40 years old but I feel incredibly well and I am holding my own, no problems whatsoever," he added.
"I feel incredibly fit and I love playing football. As long as I am playing well enough at this level I will continue to play.
"The aim is to continue to get better; I don't want to stop getting better. If you stop getting better then it is a downward slippery slope."
Schwarzer became aware of Chelsea's interest towards the end of last season before signing a one-year deal earlier this month after speaking to Mourinho.
The veteran will compete with Czech Republic goalkeeper Petr Cech for the No 1 jersey, but will likely begin the season as second choice.
Nevertheless, he is determined not to spend the campaign sitting on the substitutes' bench.
"Before I spoke to the manager I had some doubts, but once I spoke to the manager those doubts disappeared pretty quickly," Schwarzer said.
"The amount of games Chelsea play there is going to be opportunities to play games and that's also important for me."