Pulisic’s £58 million (€64m/$73m) move from Borussia Dortmund to Chelsea was confirmed on Wednesday, with the winger re-joining the German side on loan for the remainder of the 2018-19 season.
Liverpool had previously expressed an interest in signing the 20-year-old but distanced themselves from a move in November.
When asked about the deal, Klopp acknowledged that Pulisic is a unique talent but also hinted that his former side Dortmund had done well to earn so much money from the transfer.
Speaking ahead of Liverpool’s trip to champions Manchester City on Thursday, Klopp told reporters: "Really good player for Chelsea. A skilled boy. I've known him for a while, good signing, good deal as well for Dortmund.”
Commenting about the move Chelsea director Marina Granovskaia said Chelsea had signed “one of Europe’s most sought-after young players.”
"Christian has shown his quality during a fantastic spell in Germany and at just 20, we believe he has the potential to become an important Chelsea player for many years to come,” Granovskaia told the club’s official website.
Pulisic, meanwhile, said he was excited by his move to west London, labelling Chelsea a "legendary club".
The Reds can extend their lead over the reigning Premier League champions in the table to double figures with a win at the Etihad, while City can close the gap at the top to four points if they emerge with a victory.
Chelsea are also back in action on Wednesday evening after securing back-to-back wins, as they host Southampton at Stamford Bridge.