Joshua added the WBA belt to his IBF title after his epic battle in April, that saw him knockout Wladimir Klitschko at Wembley in front of 90, 000 fans.
The Millennium Stadium in Cardiff can hold 80, 000 fans and Pulev, the number one IBF challenger and the IBF champion expects an explosive battle.
“October 28 can’t come soon enough,” said Joshua. “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.”
Pulev said: “Anthony is a formidable opponent. 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.