Both parties have said they are optimistic about the exploratory talks due to begin on 7 January, which would pave the way for full-blown negotiations about a coalition.
The German Chancellor's Bavarian allies, the Christian Social Union, will also be participating in the discussions.
All three parties - the CDU, SDP and CSU - formed part of the "grand coalition" that has ruled Germany since 2013.
But Europe's largest economy has been without a stable government and in a state of political limbo since September, when an election produced no overall majority - with all three parties losing seats.
This has been the longest period that Germany has failed to form a new government after an election since 1949.