Observers hope that the re-opening leads the way to better relations between the neighbours.
Both countries expressed willingness to work together to root out their common enemy following a spate of militant attacks.
The move follows a peace deal between Hizb-e-Islami and the Afghan government in September, but not everyone is in agreement.
Iran is clearly colluding with the Taliban and must be stopped, Afghan lawmakers and civil society members say.
Hundreds of Taliban, fed up with unjust war, want to join the peace process, authorities say.