Zelenskiy will arrive in London for only his second foreign visit since Russia invaded Ukraine on Feb. 24, after Sunak pledged to expand the training of Ukrainian troops to include fighter jet pilots and marines.
Britain said the training would ensure Ukrainian pilots were able to fly "sophisticated NATO-standard fighter jets in the future".
In London, he is expected to tell Zelenskiy he will accelerate the delivery of military equipment to Ukraine.
Britain has trained 10,000 Ukrainian troops brought to battle readiness in the last six months and will upskill a further 20,000 soldiers this year, the government said.
London has so far refused to deliver fighter jets, saying it was not "the right approach" for now.