As documented in The Silmarillion, Elrond was born at the refuge of the Mouths of Sirion soon before its destruction by the sons of Fëanor. He and his brother, Elros, were captured alive. Their parents feared that they would be killed, but instead they were taken up by the brothers Maedhros and Maglor.
"For Maglor took pity upon Elros and Elrond, and he cherished them, and love grew after between them, as little might be thought; but Maglor's heart was sick and weary with the burden of the dreadful oath."
J. R. R. Tolkien: The Silmarillion