The origins of the Vedic culture lie in the interaction of the proto-Indo-Iranians with the BMAC, approximately 2,000-1,800 BCE, in the area of what is nowadays northern Afganistan. From this area, the Vedic people migrated over the Hindu Kush into the Indus Valley, around 1,500 BCE.
The emergence of the proto-Indo-Iranians is part of the Indo-European migrations. These migrations started 4,000 BCE with a diffusion from their origins in the Yamna culture, which was part of the Kurgan horizon. At 2,000 BCE started the migrations out of the Eastern-European steppes.
Sources: Beckwith, Christopher I. (2009), Empires of the Silk Road, Princeton University Press chapter 1); Anthony, David W. (2007), The Horse The Wheel And Language., Princeton University Press chapters 14 & 15