He was born in Lyngseidet as a son of district physician Engebret Qvigstad (1814–1869) and Petra Krogh Wadel (1828–1905).

An interest in Sami language and culture started when he was hired at Tromsø Seminary, and he published his first of 112 academic works in 1881.

Historical works include Den kvenske indvandring til Nord-Norge (1921), about Kven immigration to Northern Norway.

His last academic work was Opptegnelser fra samenes liv, released in 1954 when Qvigstad was 101 years old.

He was an honorary member of the Société Finno-Ougrienne from 1910 and Tromsø Museum from 1926, and Festschrifts were issued for his 75th and 100th birthdays.

[1] He was a co-founder and board member of Norsk Finnemission from 1888 to 1916 and of the regional Norwegian Bible Society office from 1889 to 1910.