He was born in Håland in Stavanger county, Norway. He was the youngest of six children born to parish priest Nils Christopher Bøckman (1807–1873) and Wencke Elisabeth Dietrichson (1808–1880). He graduated with a cand.theol. degree from the University of Oslo in 1873. From 1873 to 1876 he was a teacher at Volda Teacher's College. From 1876 to 1877, he devoted his time to theological studies in Erlangen and Leipzig. He was then a chaplain in Bergen from 1877 until 1879, vicar in Skånevik from 1879 until 1890, and dean in Tromsø from 1890 until 1893. He was the bishop of the Diocese of Tromsø from 1893 until 1909, and then bishop of the Diocese of Nidaros from 1909 until 1923.
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He was appointed a Knight of the Order of St. Olav in 1894 and got Commander Cross in 1904. He died in Oslo on 23 May 1926. He was married to Beata Jervell (1878–1926) and was a grandfather of scholar Peter W. K. Bøckman Jr. and journalist Knut Bøckman.[3]
