Joshua's promoter, Eddie Hearn, said a crowd of 80,000 was expected for the fight.
"October 28, will come not soon".
"Now I've got that strap on my back and that lion fur on my back, you walk with confidence, but before then you're a contender and you can only find out how good you are when you are put in the lion's den", said Joshua.
Joshua, who also holds the WBA and IBO titles, has been told he must face IBF mandatory challenger Pulev before December 2 or risk being stripped of that belt.
The fight comes six months after Joshua, 27, beat Wladimir Klitschko at Wembley to add the WBA title to his IBF and IBO belts.
Joshua's meeting with Pulev is set to be the fourth night of boxing held at Wales' national stadium.
Challenger Pulev's only career defeat came against Klitschko in November 2014 and aims to leave Joshua "no chance" in Cardiff.
The Klitschko rematch would have been flawless for Joshua but the Pulev fight is a real problem.
Pulev, 36, who revealed the news himself on Monday, said: 'We will not hug and hold, we will not run. "But his style fits perfectly on mine".
Pulev (25-1) has lost just once, but tellingly that was to the man Joshua defeated at Wembley in front of 90,000 fans. "However, by his own admission, he is still learning and Pulev is not the sort of opponent you want to learn against".
WBA champion Anthony Joshua has admitted that he is very occupied with his training regime which doesn't leave him much time for girlfriends, hinted he may not settle down for 10 years.
An announcement on ticket prices and on-sale dates will be made this week and the first undercard fights will be released in the coming days.