The document by the UN refugee agency, UNHCR, says the number of people forced to flee their homes rose by 8.3 million from the previous year.
The continuing conflict in Syria is seen as a major factor behind the record numbers.
UNHCR head Antonio Guterres told the BBC the "world is a mess".
"The drama is that if people think that humanitarians can clean up the mess. It's no longer possible. We have no capacities to pick up the pieces.
"More and more people are suffering, and unfortunately for many of them there is no chance to support them."
Mr Guterres said that the number of displaced people had increased to 42,500 per day in 2014 from 32,000 the year before.
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The report says that at least 15 conflicts have erupted or reignited in the past five years, including eight in Africa and three in the Middle East.
This led to 59.5 million displaced people by the end of 2014 and 19.5 million refugees.
More than 50% of these refugees were children.
UNHCR said there were 38.2 million internally displaced people, with wars in Ukraine, Nigeria and South Sudan swelling the figures.
In Syria alone, there were 3.9 million refugees and 7.6 million internally displaced persons.
The next biggest sources of refugees were Afghanistan and Somalia.
The document says that 1.8 million are still awaiting the outcome of asylum claims.
It also points to a 50% rise - to 6.7 million - of displaced people across Europe, which is struggling to deal with a growing crisis of migrants crossing the Mediterranean.
The UNHCR says Germany had the highest number of asylum applications among the 28-member European Union, followed by Sweden.
The authors of the report say their findings mean that one in every 122 people on the planet were either a refugee, internally displaced or seeking asylum.
The report's data corresponds to the findings by the EU's Eurostat, which were released earlier this year.
The number of people displaced by war, conflict or persecution reached a record high of nearly 60 million around the world in 2014, a UN report says.