The decision, adopted by Merkel's right-left coalition cabinet, must still be formally approved by President Joachim Gauck.
But the announcement fires the starting gun for an election campaign that Merkel has said will be her toughest yet due to opposition to her liberal asylum policy.
Merkel, 62, is nevertheless the clear frontrunner in the race and enjoys solid popularity in Europe's top economy.
A poll released Wednesday showed her conservative Christian Union bloc (CDU/CSU) as the strongest political force in the country with 38 percent.
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The right-wing anti-immigration Alternative for Germany (AfD), which has railed against Merkel's decision to let in more than one million asylum seekers since 2015, lost one percentage point compared to last week to reach 11 percent.
The head of the Forsa opinion research institute which conducted the poll, Manfred Guellner, said a jihadist attack on a Berlin Christmas market last month that killed 12 people and was committed by a rejected asylum seeker had failed to boost support for the AfD.
"It is actually losing support while the CDU/CSU and the SPD are stabilising."
The AfD, born as a eurosceptic party in 2013, has attempted to harness public unease with migration and asylum and, due to its relative strength, threatens to scramble the potentially complicated arithmetic of coalition building after the election.
It hopes to become the first populist party to gain seats in the Bundestag lower house of parliament in post-war Germany.
The AfD, seeking to gain momentum from a surge of European radical parties, will host a meeting of far-right leaders in the western city of Koblenz on Saturday.