Joshua returns to the ring following his epic battle with Wladimir Klitschko at Wembley Stadium in April, where he added the WBA belt to his IBF strap, in front of a record-breaking crowd of 90,000.
Cardiff's Principality Stadium - previously known as the Millennium Stadium - will hold close to 80,000 when Joshua takes on experienced Pulev and 'AJ' is looking forward to another explosive heavyweight show.
"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 is Joshua's IBF No 1 challenger and will get a second crack at becoming a world champion.
The Bulgarian, known as 'The Cobra', took on Wladimir Klitschko for the same belt back in November 2014, but is confident he can go one better this time.
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."
The confirmation ends months of speculation about who and where Joshua will fight next following Klitschko's retirement, and promoter Eddie Hearn is expecting another spectacular show and record-breaking crowd.
Eddie Hearn 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.
"Anthony will meet his mandatory challenger, No 1 ranked Kubrat Pulev and the card will be stacked with world championship action, domestic title fights and the very best young stars in the game. Get ready for the next episode from the biggest star in world boxing."
Pulev is a two-time European heavyweight champion and started his climb towards the top of the IBF rankings by out-pointing Britain's Dereck Chisora in May 2016.
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