Adalbert Wirz was the younger brother of Theodor Wirz, the son of Franz Wirz, nephew of Simon Ettlin and great-nephew of Nicholas Hermann. All four were - just as he is - Landammänner the canton Obwalden.
Wirz visited the College in Sarnen and the St. Michael's College in Freiburg. He then completed a law degree in Freiburg, Basel, Zurich and Heidelberg.
Wirz married in 1879 Rosalia Ettlin, Simon Ettlin daughter.
From 1876 to 1901 Wirz was the Civil Court President and 1910-1925 President of the Supreme Court of the Canton. He was also from 1910 to 1918 worked as a Substitute at the federal courthouse.
From 1885 to 1925 Wirz was sitting in Obwalden canton deputy, which he chaired in 1886 and 1912. As a Councillor of the Canton of Obwalden, he worked from 1901 to 1910. 1902, 1904, 1906 and 1908, he held the office of Landamman. The Senate, in which he sat from 1902 to 1925, presided over the Catholic- conservative politicians in 1906.
Wirz was a regular employee, and from 1879 to 1882 editor of Obwalden Volksfreund. From 1885 to 1892 he was president of the Swiss Pius Association and 1899-1902 of the Swiss Catholic Association. From 1912 to 1917 Wirz was the first president of the Swiss Conservative People's Party. He also presided 1917/1918 the International Catholic Union.
Wirz was a knight of the Papal Order of Pius and received in 1918 an honorary doctorate from the University of Freiburg.