Mr Biden arrived at Stansted Airport late on Sunday evening on his way to the two-day Nato summit in Lithuania on Tuesday.
At Windsor Castle, he will receive a Guard of Honour and the Band of the Welsh Guards will play the US national anthem.
The king will accompany Mr Biden to inspect the Guard before watching the military march past, before both men have tea together.
They will also join delegates at the Climate Finance Mobilisation Forum, being held on Monday.
The forum brings together finance and philanthropic leaders from the UK and the US to strengthen their commitments to climate action in emerging markets and developing economies.
But Mr Biden's decision to send cluster munitions to Ukraine could overshadow his visit to the UK.
The Democrat leader will leave behind criticism over his latest choice of ammunition for Kyiv, which has led to furious members of his own party trying to block it.
The White House on Friday announced that Mr Biden had approved the transfer of cluster bombs to Ukraine.
Lord Ricketts, the UK’s first national security adviser, told Sky News that Nato allies were “all very uncomfortable with this” decision.
“It is a hard choice of the kind that countries have to make in wartime,” he said. “I am uncomfortable with it. Yes, I wish it wasn’t being done, but I think we can understand why they are doing it.”
US President Joe Biden visits the UK - in pictures
Labour's shadow chancellor Rachel Reeves told Sky News that cluster bombs were not “appropriate weapons” to send to Ukraine.
The UK is one of more than 120 signatories to the Convention on Cluster Munitions, which bans the manufacturing, use, transfer and stockpiling of cluster munitions.
The US, Ukraine and Russia are not signatories of the international convention.
Campaigners say civilians account for the vast majority of casualties caused by such weapons.
Unexploded cluster munitions from decades ago are still lying dormant in Vietnam and Laos, according to the Cluster Munition Coalition.
The activist group, which is trying to have the weapons banned everywhere, say they are dropped from aircraft or fired from the ground or sea, opening in mid-air to release hundreds of submunitions that can saturate an area the size of several football pitches.
The coalition said sometimes “large numbers of the submunitions fail to function as designed, and instead land on the ground without exploding, where they remain as very dangerous duds”.
Barbara Lee, a Democrat congresswoman representing California, condemned Mr Biden’s decision, saying she was alarmed at the thought of cluster munitions being used in Ukraine.
“The US and Ukraine don’t need to stoop to [Russian President Vladimir] Putin’s level,” Ms Lee tweeted.
Democrats representatives Ilhan Omar of Minnesota and Sara Jacobs of California on Friday introduced an amendment that would effectively block the transfer of these munitions.
“The innocent victims of the cluster munitions will almost exclusively be Ukrainian civilians,” Ms Omar said.
She said the use of cluster bombs was a breach of human rights.
“We have to be clear: if the US is going to be a leader on international human rights, we must not participate in human rights abuses,” Ms Omar said.
Bill Richardson, who was energy secretary and UN ambassador during theadministration of president Bill Clinton, also voiced his disapproval of Mr Biden’s latest move.
Mr Richardson told CNN he would have advised Mr Biden against the decision if he was in his administration.
“I worry about civilians, non-combatants getting exposed to this,” he said. “So I’m concerned. I don’t know who advised the President on this.”
Mr Sunak and Mr Biden put on a united front at a joint press conference at the White House last month. But behind the scenes there are tensions.
The US leader is understood to have blocked UK Defence Secretary Ben Wallace's bid to become Nato's next secretary general over the fact that he once served as a British soldier in Northern Ireland.
Mr Biden, who has Irish ancestry, has made no secret of his support for Ireland and has been accused by some figures of showing a hatred for Britain.
US donations of cluster bombs for Ukraine are likely to feature heavily in discussions between Nato's 31 member states.