They included over 970,000 who made the dangerous journey across the Mediterranean.
Three-year-old Aylan died in September after his family, sheltering in Turkey from the war in Syria, decided to make a desperate bid to reach Greece in a flimsy inflatable boat.
Shocking images of the toddler washed up and face down on the shore helped spur European nations to seek an effective response to the growing migrant crisis.
"My message is I`d like the whole world to open its doors to Syrians. If a person shuts a door in someone`s face, this is very difficult," Abdullah Kurdi says in the video message.
"When a door is opened they no longer feel humiliated," he adds, according to a transcript released by Channel 4.
Aylan`s mother Rihana and brother Ghaleb, 4, died in the same accident and were buried in the Syrian town of Kobane in September, days after the tragedy.
Abdullah Kurdi had been trying to escape along with his family and up to three other Syrians from the flashpoint town, which was last year the site of a months-long battle between Kurdish militias and jihadists.
"At this time of year I would like to ask you all to think about the pain of fathers, mothers and children who are seeking peace and security," says Kurdi who now lives in Erbil in Iraq.
"We ask just for a little bit of sympathy from you."
Thousands perished
The UNHCR said that of the million who reached Europe in 2015, about half were Syrians fleeing the country`s brutal civil war.
"The number of people displaced by war and conflict is the highest seen in Western and Central Europe since the 1990s," it said, referring to conflicts in the former Yugoslavia.
In a sign that the crisis shows no sign of abating, at least 10 migrants including five children died Wednesday when their boat sank near the Greek Aegean island of Farmakonissi, the national ANA news agency said.
Another 13 people were rescued and two more are feared missing, the agency said.
And on Tuesday, the Italian coastguard said that nearly 800 people had been pulled to safety in the Mediterranean as they attempted the crossing, and one body recovered.
Greece was by far the leading landing spot for migrants to Europe this year, with 821,008 arrivals including 816,752 by sea, the International Organization for Migration said this week.
A total of 3,692 migrants died or disappeared crossing the Mediterranean this year, it added.
EU leaders have set an end-of-June deadline to agree on a new border and coastguard force to slow the influx of migrants across the 28-nation bloc`s porous external frontier.
They have also called for the rapid delivery of a promised 3.0 billion euros ($3.25 billion) in aid for refugees in Turkey in return for its help in stemming the flow.
Life is a struggle for most Syrians in Turkey, who live mostly off odd jobs that are often insufficient to feed and house a family.
Following a slew of emergency summits this year, EU leaders have acknowledged they were too slow to carry out a joint strategy to tackle Europe`s worst refugee crisis since World War II.
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