Of course I knew what your answer would be. Not an expert on ancient history or religions, but do know what Genesis 2:24 says. That's fairly ancient.
It dates to the rise of the Judeo-Christian-Islamic culture of the Middle East. That culture created what we consider marriage today, using their religious text (that you cite) as grounds.
Could you give a rough date?
Well the Old Testament has been dated to be about 6,000 years old so I guess that would be a good place to start. As Judaism is a monotheistic, androcratic religion maybe that was the start.
If you are really interested start looking at when we went from a hunter/gatherer culture/society to an agrarian culture/society. Also compare the marriage history of the Greco/Roman area with marriage history of the Celts, Germans, and Norse in their area.