Son of David Boswell (1640-1712) and Anna Hamilton (d. 1711). The paternal grandfather of James Boswell (1740-1795). Married (1704) to Elizabeth Bruce. Father of Veronica, David (1706-1709), Alexander, John, James and David (1711-1712).

As his son Alexander (d. 1782), James Boswell (d. 1749) also studied law at Leyden University in Holland. Following his wife's death in 1734 he fell into a constant melancholy and spent most of his time on religious (Presbyterian) occupations. He was also active in the renovation of the church in Auchinleck and participated in the selection of ministers for the parish.