The American winger joined his new teammates in Japan on Tuesday after competing in the Gold Cup.
Pulisic told GAFFER Magazine: 'When I think of this club, there's a lot of great players that come to mind.
"I grew up watching Frank Lampard and all of those guys at the top of their game in the Premier League and in the Champions League.
"To me, Chelsea were always one of the biggest teams and now to be playing here, it's really come full circle from that moment. It feels amazing."