The same question has been asked by Yudhishthira to Bhishma in Mahabharata, Anushashana Parva, SECTION XCI.
"Yudhishthira said, 'By whom was the Sraddha first conceived and at what time? What also is its essence? During the time when the world was peopled by only the descendants of Bhrigu and Angiras; who was the muni that established the Sraddha? What acts should not be done at Sraddha? What are those Sraddhas in which fruits and roots are to be offered? What species' also of paddy should be avoided in Sraddhas? Do thou tell me all this, O grandsire!'
Then, Bhishma told him that, there was a Rishi Atri, who had a son Dattatreya who had a son Nimi whose son was Shrimata. Shrimata died before his father. So Nimi performed purificatory rites and invited seven Brahmana and offered them foods and by mistake he offered food to his dead son. But after that Nimi filled with regret because no one has ever performed this kind of rite. He remembered Sage Atri, so Sage Atri came there and told him that what he has done is right.
"Bhishma said, 'Listen to me, O ruler of men, as I tell thee how the Sraddha was introduced, the time of such introduction, the essences of the rite, and the Muni who conceived it. From the Self-born Brahman sprang Atri, O thou of Kuru's race. In Atri's race was born a Muni of the name of Dattatreya. Dattatreya got a son of the name of Nimi possessed of wealth of asceticism. Nimi got a son named Srimat who was endued with great beauty of person. Upon the expiration of a full thousand years, Srimat, having undergone the severest austerities, succumbed to the influence of Time and departed from this world. His sire Nimi, having performed the Purificatory rites according to the ritual laid down in the ordinance, became filled with great grief, thinking continually of the loss of his son. Thinking of that cause of sorrow the high-souled Nimi collected together various agreeable objects (of food and drink) on the fourteenth day of the moon. The next morning he rose from bed. Pained his heart was with grief, as he rose from sleep that day--he succeeded in withdrawing it from the one object upon which it had been working. His understanding succeeded in busying itself with other matters. With concentrated attention he then conceived the idea of a Sraddha. All those articles of his own food, consisting of fruits and roots, and all those kinds of staple grains that were agreeable to him, were carefully thought of by that sage possessed of wealth of penances. On the day of the New moon he invited a number of adorable Brahmanas (to his asylum). Possessed of great wisdom, Nimi caused them to be seated on seats (of Kusa grass) and honoured them by going around their persons. Approaching seven such Brahmanas whom he had brought to his abode together, the puissant Nimi gave unto them food consisting of Syamaka rice, unmixed with salt. Towards the feet of those Brahmanas engaged in eating the food that was served unto them a number of Kusa blades was spread out on the seats they occupied, with the top ends of the blades directed towards the south. With a pure body and mind and with concentrated attention, Nimi, having placed those blades of sacred grass in the way indicated, offered cakes of rice unto his dead son, uttering his name and family. Having done this, that foremost of Munis became filled with regret at the idea of having achieved an act that had not (to his knowledge) been laid down in any of the scriptures. Indeed, filled with regret he began to think of what he had done. 'Never done before by the Munis, alas, what have I done! How shall I (for having done an act that has not been ordained) avoid being cursed by the Brahmanas (as an introducer of strange rites)?' He then thought of the original progenitor of his race. As soon as he was thought of, Atri endued with wealth of penances came there. Beholding him exceedingly afflicted with grief on account of the death of his son, the immortal Atri comforted him with agreeable counsels. He said unto him, 'O Mini, this rite that thou hast conceived, is a sacrifice in honour of the Pitris. Let no fear be thine, O thou that art possessed of the wealth of asceticism! The Grandsire Brahman himself, in days of old, laid it down! This rite that thou hast conceived has been ordained by the Self-born
himself. Who else than the Self-born could ordain this ritual in Sraddhas? I shall presently tell thee, O son, the excellent ordinance laid down in respect of Sraddhas. Ordained by the Self-born himself, O son, do thou follow it.
So, according to Mahabharata, Nimi was the first to perform the Shraaddha ritual.