Joshua, 27, had been pursuing a Las Vegas rematch with Wladimir Klitschko, who he beat at Wembley in April, only for the Ukrainian to announce his retirement.
Instead, Joshua (19-0) will face IBF mandatory challenger Pulev beneath a closed roof in Cardiff, paving the way for him to make his United States debut next year.
“October 28 can’t come soon enough,” Joshua said in a press release issued by Matchroom Boxing.
“I have been eager to get back in the ring since Wembley and now we are confirmed and ready.
“I’ll be locked away focusing on fight number 20 for the next eight weeks. I am excited to experience the atmosphere in a sold-out Principality Stadium and aim to give the fans a spectacular night.”
Joshua’s promoter, Eddie Hearn, said a crowd of 80,000 was expected for the fight.
Pulev, 36, lost his only previous world title fight to Klitschko inside five rounds in November 2014.
“We will not hug and hold, we will not run. We will stand and fight,” vowed Pulev (25-1).
“His style fits mine perfectly and in boxing, styles make fights. My preparation will be very intense and I will be perfectly ready when I enter the ring so that he will have no chance to beat me.”