Iran Press/ Europe: The UK announced on Thursday that it would supply Ukraine with the long-range missiles it had requested to fight against Russia.
Zelensky has been meeting Western leaders in recent days seeking to bolster support for Ukraine.
"The UK is a leader when it comes to expanding our capabilities on the ground and in the air. This cooperation will continue today," he said on Twitter.
No 10 said Sunak would reiterate the importance of providing a full package of support to Ukraine during the talks at Chequers, the prime minister's official country residence.
"We must not let them [Ukraine] down," the prime minister said, adding it was "a crucial moment" in Ukraine's war effort.
Downing Street said the UK would confirm "hundreds" of air defence missiles and drones to help Ukraine's defence later today.
It is expected that the meeting between the two leaders will not last more than a couple of hours.
Mr Zelensky's trip to the UK will be the fourth stop on a European tour that included meetings in Paris, Berlin and Rome.
Ukraine secured a new defence aid package worth €2.7bn (£2.4bn) from Germany after talks in Berlin with Chancellor Olaf Scholz on Sunday.
Zelensky described the new tranche of German Leopard tanks and anti-aircraft systems as "the largest since the beginning of the full-scale aggression" by Russia in February 2022.
Later, France promised dozens more light tanks and armoured vehicles after President Emmanuel Macron met his Ukrainian counterpart in Paris.
In February, Zelensky visited London for the first time since the start of the war, during which he attended an audience with the King and addressed Parliament.
His visit to the UK comes ahead of a G7 gathering in Hiroshima, Japan, later this week which will also be attended by Rishi Sunak.
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