Who was the first to use the Hijri calendar in Islam?

The well-known account is that the first to establish dating by the Hijra in Islam was Umar ibn al-Khattab, may Allah be pleased with him, in the seventeenth year of the Hijra. This was when he gathered the people after Abu Musa wrote to him about letters that lacked dates. Some suggested dating from the time of the Prophetic mission (Mab'ath), while others suggested dating from the Hijra. Umar then said, "The Hijra separated truth from falsehood, so date by it." Then they agreed to start with Muharram because it is when people return from their Hajj pilgrimage.