Bulgarian challenger Pulev picked up a shoulder injury in training and was told by doctors he would not be fit for the Principality Stadium fight on Saturday, October 28.
WBA and IBF heavyweight champion Joshua will now defend against Frenchman Takam, who was next in line in the IBF rankings for a mandatory shot.
Joshua’s promoter Eddie Hearn desperately tried to keep the show on with almost 80,000 fans expected at the Cardiff stadium.
They secured the signature of Takam just hours after Pulev pulled out and Joshua’s team agreed to the late change.
Pulev had suffered a shoulder injury during a sparring session in his training camp in Germany.
His management team Sauerland did not inform fight promoter Eddie Hearn straight away as they hoped the fight would go ahead.
Joshua was set to fight mandatory challenger Pulev to defend his WBA and IBF heavyweight titles.
It will be the London-born boxer’s first bout since he beat Wladimir Klitschko by knockout in a thrilling fight at Wembley in April.
Pulev had earned a shot at Joshua by winning 25 of his 26-career fights, 13 of which were by knockout.
His only defeat came against Klitschko in 2014.
But Takam will now take to the ring with 70,000 tickets already sold.
The stadium in the Welsh capital can hold 78,000 people – and it is expected to sell out as the build up intensifies this week.
Joshua has won all of his 19 professional fights by knockout and is well on track to become the greatest heavyweight champion of all time.