The magazine cited her role in Europe's crises over migration and Greek debt.
Ms Merkel had provided "steadfast moral leadership in a world where it is in short supply", editor Nancy Gibbs wrote.
Islamic State leader Abu Bakr al-Baghdadi was named runner-up and third place went to US presidential hopeful Donald Trump.
Eclectic list
Ms Gibbs wrote of Mrs Merkel: "For asking more of her country than most politicians would dare, for standing firm against tyranny as well as expedience and for providing steadfast moral leadership in a world where it is in short supply, Angela Merkel is 'Time's Person of the Year'."
Citing the refugee and Greek economic crises, along with the Paris terror attacks, Ms Gibbs said: "Each time Merkel stepped in. Germany would bail Greece out, on her strict terms. It would welcome refugees as casualties of radical Islamist savagery, not carriers of it.
"And it would deploy troops abroad in the fight against ISIS [Islamic State]. You can agree with her or not, but she is not taking the easy road. Leaders are tested only when people don't want to follow."
Ms Merkel joins an eclectic list of former winners, including Adolf Hitler, Joseph Stalin, Mahatma Gandhi, Winston Churchill and Richard Nixon.
She is only the fourth woman since 1927 to be named winner and the first in 29 years.
Last year's award went to medics fighting the Ebola outbreak in western Africa.
Time Person of the Year 2015
Angela Merkel
Abu Bakr al-Baghdadi
Donald Trump
Black Lives Matter
Hassan Rouhani
Travis Kalanick
Caitlyn Jenner
Fuente: www.bbc.com
