He grew up in Tistedalen outside Frederikshald. His father Theodor Christian Haagaas [no] (1823–1899) was the sawmill director (1862–1892) of Norway's largest timber company, Saugbrugsforeningen, and a shipowner; the elder Theodor was born on the farm Haagaas (from Old Norse Haukáss, "hawk hill") in Trøgstad, which his family had owned at least since 1555. His mother Nora was born in Norway to Swedish immigrant parents of Forest Finnish heritage, and died early. His father later lived at Veden Manor, which had previously belonged to Theodor's maternal grandfather. Theodor Haagaas was one of the pioneers of skiing in Tistedalen around 1885–1886.^[4]

In 1908 he married his former pupil Henriette Wegner Paus (1879–1942), a teacher at Nissen's Girls' School who had attended the Royal Frederick University, a rarity for a woman in the early 20th century. She was the daughter of Bernhard Pauss and Henriette Pauss (née Wegner), major figures in the development of girls' education in Norway and long-time owners and leaders of Nissen's Girls' School, and the granddaughter of the industrialist Benjamin Wegner and Henriette Wegner (née Seyler), one of the co-owners of Berenberg Bank. Theodor and Henriette were the parents of four daughters, among them the journalist, humanist and resistance fighter Henriette Bie Lorentzen (née Henriette Wegner Haagaas).^[5][6] A blue plaque, placed by Oslo Byes Vel, commemorates his daughter Henriette at Riddervolds gate 9, where the family lived from 1912.

He was the uncle of the publisher Henrik Groth and the brother-in-law of Nikolai Nissen Paus, George Wegner Paus and Augustin Paus.

He attended the Frederikshald Gymnasium and graduated with the examen artium university entrance exam in 1891. He subsequently studied philosophy, mathematics, natural sciences and law at the Royal Frederick University. He also served as a lieutenant in the Royal Norwegian Navy 1898–1902.

From 1900 he was a lecturer in mathematics at the private gymnasium Frogner School in Oslo. In 1911 he became a member of the management of the school and in 1913 he became one of the school's co-owners. At the time Frogner School's neighbour, the Nissen's Girls' School, was also owned by Frogner School, although they operated as separate schools. He and the other owners sold both schools to Christiania municipality in 1918 and continued to manage them until 1919. In 1917 he was appointed by the King-in-Council as a lecturer at Drammen Higher School,^[7] and took office in 1918. In 1920 he left this position to become a lecturer at Frogner School again.

In 1915 he founded Haagaas School, a private gymnasium in Oslo that existed until 1955, and was the school's headmaster until 1946. Haagaas School was the last school in Norway in the tradition of the Heltberg School of the 19th century, offering a fast track to the examen artium (a so-called studentfabrikk, "student factory" or intensive gymnasium). The noted educator Mosse Jørgensen wrote that "if any school had deserved the epithet 'The New Heltberg', it was Haagaas School."^[1] According to his former pupil Harald Throne-Holst, Haagaas was characterized by a "strong and active sense of humor."^[8] The journal Den høgre skolen (The Higher School) noted that:

Throughout his teaching career, he worked primarily at Frogner School in Oslo, where he was a central and unifying figure ... his main subject was mathematics. All of his students remember him as an outstanding teacher; they feared and loved him, and they reveled in his incomparable humor. He must have been the ideal math teacher. He possessed great authority, was conscientious and meticulous, practical and down-to-earth, patient, clear, and concise. And he had a sense of humor! Along with all these qualities, he was also quite the humanist – a humanist of the classical type.

— Den høgre skolen (The Higher School)^[9]

He was a co-author and subsequently the sole author of the Haffner og Haagaas series of textbooks in mathematics, which was published between 1925 and 1979 in numerous editions. He was one of the handful of government-appointed examiners in mathematics at the examen artium university entrance exams for several decades. On his death he was described by Aftenposten as a "very widely known educator."^[2]

• King's Medal of Merit in Gold, 1949, for services to education and for fostering culture and Bildung in wide circles of society^[10][3]