Authority President Mahmoud Abbas.
The Israel-Palestinian conflict is likely to be at the core of the talks with Mr Abbas.
The American leader will only spend a few hours in Ramallah, before heading to Jerusalem to give a speech.
Mr Obama made his first trip to Israel as president on Wednesday, holding talks with PM Benjamin Netanyahu.
The two leaders reaffirmed their commitment to a two-state solution to the Israel-Palestinian conflict.
Speaking in Jerusalem, Mr Obama said a central element of securing a lasting peace in the Middle East "must be a strong and secure Jewish state where its security concerns are met, alongside a sovereign and independent Palestinian state".
Meanwhile, Israeli police said two rockets had been fired from Gaza into southern Israel on Thursday morning.
There have been no reports of injuries or casualties.'Intolerable'
The BBC's Jon Donnison in Ramallah says the West Bank meeting could prove a difficult corner to turn, after Mr Obama also declared that the US was Israel's strongest ally.
Barack Obama in Middle East
Wednesday: Meets Benjamin Netanyahu
Thursday: Meets Mahmoud Abbas, addresses Israeli students
Friday: Visits Bethlehem's Church of Nativity and later departs for Jordan
Palestinians have been disappointed with the American leader and expectations are low, our correspondent says.
In a 2009 speech in Cairo, Mr Obama called the situation for Palestinians "intolerable" and spoke of their undeniable suffering in pursuit of a homeland.
Since then, however, little has changed on the ground as the Middle East's most intractable conflict has been sidelined by the Arab Spring, and US-Israeli concern over Syria and Iran, our correspondent says.
Following the talks in Jerusalem, Mr Netanyahu said his new government, sworn in earlier this week, remained "fully committed to peace and the solution of two states".
"We extend our hands in peace and friendship to the Palestinian people," he said, adding that he hoped Mr Obama's visit would "turn a page" in relations with the Palestinians.
But the two leaders also said they agreed that Israel had the right to "defend itself by itself".
Mr Obama and Mr Netanyahu said they agreed Israel had the right to "defend itself by itself"After his trip to the West Bank, Mr Obama is expected to deliver a speech to Israeli students in Jerusalem. He will leave for Jordan on Friday.
Security for his three-day visit is tight, with thousands of Israeli and Palestinian security officers on duty in Jerusalem and Ramallah, the Palestinians' de facto capital.
Both Israeli and Palestinian groups have staged protests in the run-up to Mr Obama's visit.
There were clashes in Hebron in the West Bank between Israeli settlers and pro-Palestinian protesters calling for an end to "apartheid", and in Gaza City protesters burned US flags outside UN offices.
Meanwhile, Israelis have staged protests in Jerusalem demanding Mr Obama free Jonathan Pollard, imprisoned in the US in 1987 for spying for Israel.
