The bout is scheduled for October 28th at Cardiff’s Millennium Stadium, with more than 70,000 tickets already sold.
It will be Joshua’s first fight since stopping Wladimir Klitschko at Wembley in April, adding the WBA title to the IBF belt he claimed in 2016.
Bulgarian Pulev suffered a shoulder injury in sparring, with Cameroonian-French fighter Takam the next in line.
New Zealand heavyweight and WBO world champion Joseph Parker beat Takam in May last year in the IBF eliminator to claim the mandatory rights to fight for the belt which is held by Joshua.
However Parker went on the beat Andy Ruiz for the vacant WBO heavyweight world title, meaning he had to give up his spot as the IBF’s mandatory challenger.
The 36-year-old Takam had been on standby for the Joshua fight, promoter Eddie Hearn said.
“I received a call from [promoter] Kalle Sauerland late afternoon to inform me that Pulev had injured his shoulder and may be ruled out of the fight – this was later confirmed by his doctor,” he added.
“IBF rules state that the mandatory will go to the next fighter in line which is Carlos Takam.
“When the Pulev fight was announced I made a deal with Takam’s team to begin camp and be on standby for this fight.
“When I called them this evening they were overjoyed and good to go. It’s a difficult position for AJ – having prepared meticulously for the style and height of Pulev, he now faces a completely different style and challenge in Takam.
“This hasn’t happened in his career before but he is ready for all comers on 28 October.”