The Blues recovered from last season's 10th-place finish to win the league in Antonio Conte's first year in charge and can make it a double when they take on their London rivals in Saturday's final. Arsenal, meanwhile, are playing to save their season after falling out of the top four for the first time in 21 years.
Zouma will likely be on the bench at Wembley as backup to Cesar Azpilicueta, but he insists Chelsea are not in party mode just yet and are prepared for one more huge game.
"It feels good," Zouma told the Chelsea Podcast at the club's FA Cup final media day. "We had a good season, we are champions and we are in the final of the FA Cup, but we are going to Wembley to win the double. It means a lot [to have a successful season after finishing tenth].
"We wanted to bounce back. We won the league and we are very happy with that but we have another difficult game to play and if we get the double, it will be good for us. We have forgotten already last season.
"The last game I played, I played on the right side. I feel great. We do a lot of tactical work, watch a lot of videos and everybody knows what to do. We are confident, we have a strong team but they have a strong team also.
"We haven't won the game yet, we haven't played yet. We are focused. We know it is going to be difficult. We know it is just one game, one final and we know that finals are always tough.
"Especially when at Wembley. A big crowd, the stadium will be full and it is a London derby. So let's see what's going on there but we are ready to win."
Conte has surprised many by turning Chelsea around this season, while he showed his faith in Zouma as he kept him in the squad his near year long absence due to a cruciate ligament injury.
Zouma revealed that Conte is very close to his players and lauded his manager's impact so far.
"We know he brings the Italian style," Zouma continued. "Tactically we know what to do, in our positions the way we are playing, we did a lot of tactical work with videos. Yes, [it is] the Italian style. Everything is working, let's do it again.
"It will be a great season for him and for us. He did a great job to us, he is really close to us and he has taught us a lot."