Didier Drogba's free-kick sank Portsmouth in Saturday's FA Cup final at Wembley as Carlo Ancelotti's side added that trophy to the Barclays Premier League, which they wrapped up in style with an 8-0 win over Wigan.
They celebrated with a open-top bus parade on Sunday, and Cech told Sky Sports News: "I hope this is the first achievement of a long cycle, that we will able to defend the title and compete every year to win the double.
"As well, you can't forget there is still the Champions League missing for this club. I can see this club going forward again, this is a massive moment and it can give us a lot of confidence for next year."
Looking back over the season, the Czech Republic international added: "Throughout the season there were so many things going on - we were eight points clear, we dropped that, we had to win at Old Trafford to win the title.
"We survived many difficulties, we managed to go through it and we won the double."
The normally reserved Ancelotti led the assembled Chelsea fans in song, backed by skipper John Terry.
Drogba had earlier, bizarrely, been seen sporting a bra on the bus' front seat - presumably a reference to the "two cups" won by the club.
Winger Florent Malouda said: "A moment like that where you celebrate, that's what it is all about - winning trophies and winning titles and celebrating with all the fans.
"You have been working so hard from pre-season and now, look, we have won trophies."
Midfielder Joe Cole added: "This is always a lovely day for the fans and I'm so pleased for everyone - the players, the staff and fans - we deserve everything we got this year. It's an incredible season."
But the England star, out of contract this summer, would not be drawn on his future.
"My focus is the World Cup now," he said. "I've got an opportunity to go to South Africa, I want to go there and I want to play, so that's where my full focus has to be.
"I'm going away with England Wednesday, so I'll spend time with my family, and I'm 100% focused on going to the World Cup."