The Hungarian capital is the first host city to be named under a new bidding process announced in February last year by the International Association of Athletics Federations (IAAF).
"It has been the scene of some of our greatest moments as a sport. We are excited about their plans for a new stadium that will become a great legacy for athletics," he said.
The new stadium will be built on the eastern bank of the River Danube with a capacity of 40,000 for the championships, reduced to 15,000 for future events.
Budapest has twice hosted the IAAF world indoor championships and the European athletics championships.
The 2019 world championships will be held in Doha, Qatar, and the 2021 edition in Eugene, Oregon. (Reporting by Alan Baldwin in London, editing by Ed Osmond)
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