The fight is expected to take place in March next year.
Last month Joshua was beaten by decision as he faced Usyk at the Tottenham Hotspur stadium and lost his WBA, IBF, WBO and IBO belts in process.
Hearn told DAZN: ‘Today we officially triggered the rematch for Oleksandr Usyk fight, which we’ll see early next spring.
‘Back in the game and we’re looking for him to become three-time world champion.
‘A few niggles in camp for AJ, Usyk had a bad cut, it’s officially triggered, we’ll sit down with K2 Promotions and I think March is when you’ll see that fight.
‘This was a disappointing loss to a pound-for-pound great.
‘We don’t need to get back in the game with 10-rounders, he needs to rip those belts off Usyk.’
There is uncertainty over where the fight will take place, with Usyk wanting it to be held in Kiev, the capital of his native Ukraine.
Hearn, meanwhile, is eager for the fight to be staged in the UK even though there is an option to hold it in the Middle East.