A close fight was still up for grabs going into the final round, with Joshua giving a mature display to guarantee himself at least a silver medal.
Joshua landed a sharp right early on but there was nothing to choose between the two fighters after the first round, level at four points apiece.
The Brit upped the pace in the second but could not force an advantage, the bout still level at 8-8 going into the final third.
Joshua bloodied Dychko's nose early in the last round, working behind an effective jab.
The Londoner finished strongly to edge a close decision, winning by 13 points to 11.
Joshua will now face reigning Olympic champion Roberto Cammarelle in Sunday's super heavyweight final.