But controversy over the Trump campaign's ties with Russia will loom over the talks, making any agreements unlikely.
Rarely in recent history has a meeting of two heads of state generated so much excitement, anxiety and hope.
The Kremlin views tomorrow's encounter as a watershed moment that could ease Russia-West tensions.
Some in the US, meanwhile, worry that Trump could make unjustified concessions to Russia.
Amid investigations into possible collusion with Moscow by Trump's campaign, any deal with Putin would expose Trump to more criticism.
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"If Putin comes to the conclusion that even if Russia and the US reach agreement, Trump would be unable to implement it for domestic policy reasons, he would lose interest in seeking an agreement," said Dmitri Trenin, the director of the Carnegie Moscow Center.
Putin, a KGB veteran who once described himself as an "expert in personal communications," always focuses closely on trying to establish warm ties with his counterparts. Kremlin- watchers say Putin meticulously prepares for meetings with foreign leaders, studying their track records and personal habits.
Fyodor Lukyanov, the head of the Council for Foreign and Defense Policies, said even if Putin and Trump develop a good rapport, Trump's ability to deliver on his promises will be a key factor for the Russian leader.
"If Putin has a positive view, as a minimum he will give (Trump) more time to sort things out," he said. "But he could possibly conclude that he (Trump) may not succeed in sorting things out and, moreover, doesn't really want an honest deal. If Putin decides it's not going to work, he will drop all constraints."
The Kremlin was very pleased with Trump's presidential victory, since he promised to improve ties with Russia and praised Putin during the campaign. It had hoped for a quick meeting after Trump's inauguration in January, but US congressional and FBI investigations into links between Trump campaign aides and Russia blocked an early encounter.
In the last few months, Moscow's hopes that Trump could act to lift the sanctions imposed on Russia over the Ukrainian crisis have withered. Putin and his lieutenants have also become increasingly impatient about US-Russia ties remaining at a freezing point.
Russia and the US have struggled to even set a specific time for tomorrow's meeting and the White House says there's "no specific agenda" for it.
When the two presidents finally sit down for a talk, sharp differences remain on a wide range of issues, from Syria and the Ukrainian crisis to nuclear arms control.
While Trump has said the US and Russia could pool efforts to fight the Islamic State group in Syria, Moscow's firm support for Syrian President Bashar Assad makes any agreement unlikely.
And when the White House warned last week that Assad was preparing for another chemical attack and would "pay a heavy price" if he launches it, Russia responded by offering the Syrian ruler a tour of its air base.
Bitter differences over Ukraine haven't been resolved. Some US lawmakers have been pushing the White House to approve the delivery of weapons to the Ukrainian military in response to Moscow's support for separatists in eastern Ukraine a move that would cross a red line for the Kremlin.
Also clouding tomorrow's meeting are Washington's concerns about Russian violations of a landmark Cold-War era nuclear arms deal. Moscow has rejected those claims and instead accused the US of breaching the pact.
US officials have indicated that Washington expects Moscow to make some trade-offs in exchange for the two properties, but analysts in Moscow say the Kremlin isn't prepared to bargain on this.
"I would be surprised if Vladimir Putin offers any concessions in exchange for restoring what Russia sees as its inalienable rights," Trenin said. "If no agreement is reached, Russia will take retaliatory measures, which could trigger new US moves.