Helgason was born in Álftanes, on June 21, 1866, the son of the Reverend Helgi Hálfdanarson, later the rector of the Prestaskólinn (the Icelandic Seminary), and his wife Þórhildur Tómasdóttir.

He came from a well-known family, including his grandfather Tómas Sæmundsson, a professor at Breiðabólstaður.

Jón studied at the Reykjavik School between 1880 and 1886, then completed his degree and sailed the same summer in Copenhagen, where he completed various university degrees, including in Theology in 1892.

He was taught in Reykjavík between 1892 and 1893, worked at a church in Denmark in 1893, completed two further examinations from the school in Höfn in 1894 and then travelled through Germany with a grant from the Danish government.

There he learned about the German Bible and the publications of the prehistoric liberal theology.