Meehan was born at 141 Great Britain Street, Dublin, on 12 July 1812. He received his early education at Ballymahon, County Longford, the native place of his parents. In 1828 he went to the Irish Catholic College, Rome, where he studied until he was ordained a priest in 1834. Returning to Dublin in the same year Meehan was appointed to a curacy at Rathdrum, County Wicklow. After nine months he was transferred to a curacy at the parish church of Saints Michael and John, Dublin. In that position he continued till his death, on 14 March 1890.

A friend and confessor to the poet James Clarence Mangan, Meehan encouraged him to write his autobiography. Rev. Meehan was also elected a member of the Royal Irish Academy.[