The magazine cited her role in Europe’s crises over migration and Greek debt.
Mrs 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.
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.
Time Person of the Year 2015
Angela Merkel – German chancellor since the 2005 election, leader of the CDU
Abu Bakr al-Baghdadi – head of the Islamic State militant group
Donald Trump – business magnate seeking Republican nomination as US presidential candidate
Black Lives Matter – activist group campaigning against violence towards black people, notably in the US
Hassan Rouhani – president of Iran since 2013
Travis Kalanick – US entrepreneur, founder of the Uber transportation network firm
Caitlyn Jenner – born Bruce Jenner, became 1976 Olympic decathlon champion, officially changed name and gender in 2015
“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.”
The magazine also noted her leadership during what it called Russian President Vladimir Putin’s “creeping theft of Ukraine”.
Mrs Merkel’s spokesman, Steffen Seibert, said: “I am sure the chancellor will cherish this as an incentive in her job.”
After the award was announced Donald Trump tweeted: “I told you @TIME Magazine would never pick me as person of the year despite being the big favorite They picked person who is ruining Germany.”
While Time runs a poll for readers to vote, the decision on winners is made independently by the editors.
Mrs Merkel, 61, 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 an individual winner outright and the first in 29 years.
The other individual women to win were Wallis Simpson (1936), Queen Elizabeth II (1952) and Corazon Aquino (1986).
Soong Mei-ling won jointly with her husband Chiang Kai-shek in 1937, three women won as Whistleblowers in 2002 and the award went generically to American Women in 1975.
It has gone to other generic groups in the past too, including last year’s award which went to medics fighting the Ebola outbreak in western Africa.