The Blues signed the 20-year-old in a £58million deal from Borussia Dortmund in January, but loaned him back to the German club for the rest of the season.
He will link up with his new Chelsea team-mates during their pre-season training camp.
Pulisic told the club’s website: “There are so many great players here already and I can’t wait to work with them all.
“I’m excited to play alongside N’Golo Kante, I think he’s a fantastic player and I can’t wait to meet him.
“Also there’s the guys in the backline, players like David Luiz and [Toni] Rudiger, I’m looking forward to working with them and I think it’s going to be really cool.”
Pulisic will hope to leave Germany with a Bundesliga winners’ medal.
Dortmund will win their first top-flight title in seven years if they beat Borussia Monchengladbach and Bayern Munich lose to Frankfurt this weekend.
However, the United States winger is ready to realise his ‘dream’ of playing in the Premier League.
He added: “It feels amazing and I’m super excited to get started with Chelsea.