He told the United Nations General Assembly that world leaders, notably Germany and Canada, have vowed to double the number from last year.
"We are facing a crisis of epic proportion," Mr Obama said.
About 21 million refugees have been forced to flee their countries due to conflict or persecution, the UN says.
Nine million people alone have been displaced by the six-year conflict in Syria while more than four million others have fled the war-torn country.
"We cannot avert our eyes or turn our backs. To slam the door in the face of these families would betray our deepest values," he added.
The US has agreed to take in 110,000 new refugees in the 2017 fiscal year - which begins on 1 October- compared with the 85,000 refugees it expects by the end of September.
The president's remarks come a day after a US and Russia-brokered ceasefire unravelled, partly due to a US-led air strike over the weekend that mistakenly killed Syrian soldiers.
Tensions continued on Monday when a strike, which witnesses say came from the air, hit an aid convoy at Urum al-Kubra, destroying 18 UN lorries and killing about 20 civilians.
The UN has since suspended all aid convoys to Syria in response.
Both Russia and Syria have insisted their forces were not behind the strike.
The president's announcement also included a pledge by countries to increase financial contributions to UN appeals and humanitarian groups by about $4.5b (Â£3.5b) over 2015 levels.
Participating countries have vowed to help fund schools for a million refugee children as well as assist in helping one million refugees work legally.
Mr Obama used his eighth and final UN address as president to call for a "course correction" to ensure that extremism and violence does not drive countries into a more divided world.
"Together, now, we have to open our hearts and do more to help refugees who are desperate for a home," he said.
Though he made no direct mention of the US, Mr Obama said wealthy countries with the resources should do more to help.
In what appeared to be a dig at Republican presidential candidate Donald Trump, he added: "The world is too small for us to simply be able to build a wall and prevent (extremism) from affecting our own societies."
Hours earlier, UN Secretary General Ban Ki-moon also expressed concern over the conflict in Syria, saying there was "no military solution".
"Gulfs of mistrust divide citizens from their leaders. Extremists push people into camps of 'us' and 'them'," Mr Ban said, taking the world stage for the last time as secretary general.
"The Earth assails us with rising seas, record heat and extreme storms. And danger defines the days of many."
US President Barack Obama has announced a pledge by 50 nations to take in 360,000 refugees from war-torn countries this year.