The past year -- when the top EU economy took in over one million asylum seekers - had been unusually challenging, she said in a pre-released text of the speech, also bracing Germans for more hardships ahead.
But she stressed that in the end it would all be worth it because "countries have always benefitted from successful immigration, both economically and socially".
With a view to right-wing populists and xenophobic street rallies, she said "it's important we don't allow ourselves to be divided".
"It is crucial not to follow those who, with coldness or even hatred in their hearts, lay a sole claim to what it means to be German and seek to exclude others."
Merkel has earned both praise and criticism at home and abroad for her decision to open Germany to a record wave of refugees, about half from war-torn Syria.
Germany took in almost 1.1 million asylum seekers this year, five times last year's total, the Saechsische Zeitung regional daily reported Wednesday citing unpublished official figures.
Merkel, faced with opposition in her conservative camp and popular concerns about the influx, has vowed steps to reduce numbers next year.
Her plan involves convincing other EU members to take in more refugees, so far with little success, and an EU deal with gateway country Turkey to better protect its borders.
Merkel said that "there has rarely been a year in which we were challenged so much to follow up our words with deeds".
She thanked volunteers and police, soldiers and administrators for their "outstanding" accomplishments and "doing far, far more than their duty".
Looking to 2016, she said "there is no question that the influx of so many people will keep demanding much of us. It will take time, effort and money."
But Merkel recalled that Germany had mastered past challenges such as reunification a quarter-century ago and benefitted from a "robust and innovative" economy.
"I am convinced," she said, "that, handled properly, today's great task presented by the influx and the integration of so many people is an opportunity for tomorrow."
She urged Germans to be "self-confident and free, humanitarian and open to the world".
Amid the world's greatest refugee wave since World War II, she said, "it goes without saying that we help and accommodate people who seek safe haven with us".