Francis also announced two parishes in the Vatican will offer a home to a family of refugees in the coming days.
The pontiff's announcement was met with applause from the crowd gathered to hear his Sunday address at St. Peter's Square.
It comes after more than 8,000 refugees and migrants arrived in Germany on Saturday with many more expected to follow.
Meanwhile, Chancellor George Osborne has said the UK's international aid budget will be used to help fund the Government's promised influx of "thousands more" Syrian refugees.
Mr Osborne said that the money from the UK's £12 billion-a-year aid spending will be diverted to local authorities to help them cover the costs of housing people from the refugee camps bordering Syria.
"The foreign aid budget that we have can provide the support for the first year for these refugees, to help the local councils with things like housing costs. We will deploy the foreign aid budget to help with the costs of these refugees," he said.
"We have got a £12 billion aid budget, we spend £250 million on those countries like Syria, Jordan and Turkey. We have got to have a fundamental re-think of how we are using this budget.
"This budget is tied to our GDP, our GDP is going up, let's use the additional money very specifically on the challenges that Britain faces, one of which is this crisis on our doorstep."
The Chancellor said David Cameron will set out details of the Government's plan to take more refugees - announced on Friday - in the Commons when MPs return to Westminster following their summer break on Monday.
Several Church of England bishops have already said they will offer refuge to asylum seekers arriving in Britain from Syria and Iraq.
The Bishops in the Diocese of Chelmsford and the Church of England in Essex & East London are planning to offer people fleeing conflict accomodation.
The offer comes as more than 40 councils across Britain have also agreed to offer shelter to Syrian refugees.
