Photo: Matchroom Boxing
Watford-born Joshua currently holds the WBA, IBF and WBO and faces Pulev, who is mandatory with the IBF.
The 30-year-old regained his belts with a points victory over Andy Ruiz Jr in December.
It will be the first fight in the UK for Joshua since 2018, where he beat Alexander Povetkin at Wembley Stadium.
Joshua and Pulev were due to meet in Cardiff in October 2017, but the Bulgarian withdrew after picking up a shoulder injury, with Carlos Takam coming in at just 12 days notice.
“On June 20, I am defending my Heavyweight World Titles,” said Joshua. “I’m back in my home city after some time away.
“A spectacular stadium has been built in North London and I’m honoured to bring the boxing community from all over the world to witness us make history with the stadium’s first Heavyweight World Title fight. The belts go back up in the air and nothing will stop me from being victorious.”
“I’m so excited to see Anthony Joshua return to the capital, 70,000 at the Tottenham Hotspur Stadium is going to be very special.
“2019 was a crazy year that had everything – the only thing missing was a UK fight and as we go into what I believe will be the biggest year of ‘AJ’s’ career so far, all our attention turns to Kubrat Pulev in an absolute must win fight. Pulev is undefeated in six years and his team and especially Bob Arum really fancy this. I think you are going to see something special from ‘AJ’ on June 20 – a destructive performance on the road to undisputed.”
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