The Premier League side confirmed on Wednesday that they agreed to pay €64m to sign Pulisic from Dortmund on a five-and-a-half-year contract.
The move from the Bundesliga leaders makes the 20-year-old, widely regarded as one of the world's best young players, the most expensive American player in history.
"It's a privilege to have signed for such a legendary club and I look forward to working hard towards being a contributor to their team of world-class players," Pulisic wrote on his official Twitter account.
Amidst the global headlines, Sarri conceded he had no idea the transfer was being negotiated.
"I didn't know anything about [Chelsea signing] Christian Pulisic yesterday," Sarri told BBC Sport after the goalless draw with Southampton.
"The club asked my opinion about him one month ago and my opinion was positive and I knew the deal was done [today] but I didn't know anything. I'm not in charge of the market.
On his opinion of the 20-year-old only joining the club at the end of the season; "We have to play every three days so I cannot think of next year, I have to think about the next match."