Mr Sunak said he was “humbled” to visit Ukraine, as he pledged continued British support to the country in its fight against Russia.
His arrival was accompanied by the announcement of a £50 million package of defence aid, comprising 125 anti-aircraft guns and technology to counter Iranian-supplied drones, including dozens of radar and anti-drone electronic warfare systems.
It follows more than 1,000 new anti-air missiles announced by Defence Secretary Ben Wallace earlier this month.
The UK has also bolstered its training offer to Ukrainian’s armed forces, sending army medics and engineers to the region to offer support.
Mr Sunak laid flowers at a memorial for the war dead and lit a candle at a memorial for victims of the Holodomor famine of the 1930s, before meeting emergency personnel at a fire station.
The team described their work rescuing survivors from the rubble and fighting fires in the aftermath of Russian air strikes and mortar attacks.
Mr Sunak also saw captured Iranian-made drones which have been used by the Russians in recent months.
He said it was “deeply humbling” to be in Kyiv, and he said he was “proud” of how the UK had supported Ukraine since the beginning of the war.
“I am proud of how the UK stood with Ukraine from the very beginning. And I am here today to say the UK and our allies will continue to stand with Ukraine, as it fights to end this barbarous war and deliver a just peace,” he said.
“While Ukraine’s armed forces succeed in pushing back Russian forces on the ground, civilians are being brutally bombarded from the air.
“We are today providing new air defences, including anti-aircraft guns, radar and anti-drone equipment, and stepping up humanitarian support for the cold, hard winter ahead.
“It is deeply humbling to be in Kyiv today and to have the opportunity to meet those who are doing so much, and paying so high a price.”
In a tweet, which included footage of their meeting, Mr Sunak wrote: “Britain knows what it means to fight for freedom. We are with you all the way.”
The video shows him shaking hands with the Ukrainian leader in a snowy Kyiv.
“Welcome. How are you?” Mr Zelenskyy asks the Prime Minister.
“Really good to see you,” Mr Sunak says as Mr Zelenskyy gestures at the falling snow.
The pair are shown shaking hands in front of the British and Ukrainian flags, with the pair also shown holding a one-to-one meeting.
“We discussed the most important issues both for our countries and for global security,” Mr Zelenskyy wrote on Telegram following the meeting.
“We are stronger and we will achieve the desired results.”
The Prime Minister has also confirmed £12m for the World Food Programme’s response, as well as £4m for the International Organisation for Migration. The funding will help provide generators, shelter, water repairs and mobile health clinics.
The UK is also sending tens of thousands of extreme cold winter kits for Ukrainian troops.
It has identified an initial eight construction projects to be supported by UK Export Finance, helping to repair Ukraine’s critical infrastructure and lay the foundations for economic recovery.
The projects include six bridges and two housing projects, including a development in Bucha for about 2,250 residents.
Mr Zelenskyy tweeted his thanks to Mr Sunak: “With friends like you by our side, we are confident in our victory. Both of our nations know what it means to stand up for freedom.”
Mr Sunak's vocal support puts him in the footsteps of Boris Johnson and Liz Truss.
The Prime Minister, who has spoken to Mr Zelenskyy on more than one occasion since entering Downing Street, used his appearance at the G20 this week to join allies and other western leaders to condemn Russia's invasion.
The visit came after a week in which tensions between the West and Russia increased when an S-300 missile killed two people in a Polish village close to the Ukrainian border, leading to accusations that Russia had fired on a Nato member state.
Tensions have eased since by the likely attribution of the hit to Ukrainian defence forces. Russian missile strikes on Ukrainian infrastructure have shown no sign of relenting.