The Blues beat off competition from Liverpool and Tottenham and look set to sign Pulisic when the January window opens, according to Daily Mail.
The US international shone for his country against England on Thursday night.
He will be out of contract in 18 months and is being chased by a host of Premier League clubs.
Daily Mail reports that Chelsea are hopeful of wrapping up a deal for a player who could command a £70million fee.
Chelsea are pushing to conclude the deal in January while the threat of a transfer ban looms over them.
The player had also spoken about moving to England before, saying, “The Premier League, is where lots of kids dream of playing so there is no reason why one day I won’t play here.
“We are having a great year at Dortmund and I am enjoying every moment of that. Then when the time comes for me to talk in the breaks about my future, that’s when those things will happen.”
