It will involve US B-52 long-range bombers, and up to 60 aircraft in total will take part in training flights over Belgium, the United Kingdom and the North Sea.
NATO Secretary General Jens Stoltenberg has rejected any calls to scrap the drill after Putin ratcheted up his nuclear rhetoric as his troops lose ground in Ukraine.
"It would send a very wrong signal if we suddenly now cancelled a routine, long-time planned exercise because of the war in Ukraine," Stoltenberg said last week.
"We need to understand that NATO's firm, predictable behaviour, our military strength, is the best way to prevent escalation."
NATO says it has seen no change in Russia's nuclear posture despite the tougher language from the Kremlin.
"But we remain vigilant," Stoltenberg said.
