The Sanskrit word 'Stupa' occurs as early as the Rigveda. In the meaning of Buddhist usage, it is divided from the Pali word 'thup', or heap in a dome like form, erected over the mortal remains of Buddha and Buddhist saints. The practice of erecting mounds over the body remains of the dead was a long established tradition, perhaps going back to prehistoric times.
After demise of the master, Buddhists accepted this age old custom of erecting stupas over the corporeal relics of the Buddha, on the advice given by the master himself. According to Buddhist literature, the relics of the Gautam Buddha were collected after his cremation and given to the eight legitimate claimants of it. In addition to body remains, the stupas used to house the daily belongings of the Buddha and his disciples.
As a result, stupas were of different categories as per their various purpose. As an architectural form, the stupa consists many parts. It is told that Asoka built 84000 stupas throughout his empire on relics, collected from the original Savirika stupas. Besides constructing new stupas, Asoka is said to have enlarged the stupa as a previous Buddha too. Excavation undertakes at Sanchi, Sarnath and Piprahava have revealed traces of nucleus stupa, built during Asoka's period. Thus we can say, Asoka himself was responsible for developing stupa-puja into a popular cult.
To whom Gautama Buddha has adviced to erect stupa over his relics (Buddha's) like the universal emperor.