The Hague (II) convention: "To kill or wound an enemy who, having laid down arms, or having no longer means of defence, has surrendered at discretion".
"Grounding arms", dropping weapons, is consistent with unconditional surrender rather than any other form of limited capitulation (a bilateral legal act, when discussion under truce would be required). It seems soldiers would only communicate an intent to surrender by throwing weapons down if they were unconditionally surrendering.
The decision to surrender can be made at any level and the responsibility to ensure voluntary disarmament, necessary for unconditional surrender as we see in the Hague conventions, belongs to the person offering the surrender. If you look in US Army regulations: "Capitulations ... Once settled, they must be scrupulously observed by both parties.". This (US interpretation of the customs of surrender) clearly communicates that it is the duty of the soldiers to abide by the surrender and, of course, for the surrender of multiple soldiers commands to "ground arms" would be required.
Wikipedia says: "A white flag or handkerchief is a common symbol of surrender, as is the gesture of raising one's hands empty and open above one's head. When a tank commander is surrendering, the tank's turret should be turned opposite the direction of the opposing forces". A method of surrendering is not specified by the Laws of War (The white flag is, but has other uses) and is probably decided on the ground by people trying not to get shot. Grounding weapons lacks clarity (when compared to raising hands, for example), even more so when concealed by cover, and is probably avoided as the sole communication of surrender by common sense rather than protocol.
Interestingly enough, in theatres of war where we can't rely on common sense, natural communication etc. to display intent to surrender, these protocols are defined and dropping weapons is discouraged as vague and inconclusive.
Manual on International Law applied to military aircraft: "Rocking the aircraft’s wings, lowering the landing gear and other signals (such as flashing of navigational lights or jettisoning of weapons) are sometimes cited as indications of an intent to surrender, but they cannot be regarded as conclusive evidence, since there may be other reasons for the activity in question. Moreover, when air and missile combat is conducted beyond visual range, as frequently happens in modern warfare, such gestures are futile. Consequently, only an appropriate radio communication — duly transmitted to the enemy, preferably on an ICAO distress frequency — may be deemed an effective message of surrender in over-the-horizon aerial encounters."