1126 GMT October 16, 2018
The fight between the 27-year-old and his Bulgarian mandatory challenger has been under negotiation since early August when his first-choice opponent Wladimir Klitschko announced his retirement, PA Sport reported.
A rematch with Klitschko would have been scheduled for November 11 in Las Vegas, which could have hosted Joshua-Pulev.
The favored venue of Cardiff instead means the champion will likely fight under the closed roof before pursuing his US debut in 2018.
There had also been suggestions the WBA could strip Joshua of their title amid their preference for him to fight Luis Ortiz, but with the Cuban likely to challenge WBC champion Deontay Wilder, Joshua's path appears clear.
Joshua said, "October 28 can't come soon enough, 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."
The 36-year-old Pulev, who lost his previous world heavyweight title fight against Klitschko inside five rounds, said, "We will not hug and hold, we will not run. We will stand and fight.
"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."
Joshua's promoter, Eddie Hearn of Matchroom, had applied for a license to promote in Nevada in his anticipation of a rematch with Klitschko, but he said, "I'm delighted that we will be in Cardiff at the magnificent Principality Stadium for the next step of the AJ journey.
"Nearly 80,000 will gather on October 28 to create another unforgettable night of boxing."