Wulff was born in Nizhyn, Chernigov province where his mother Lydia was daughter of teacher E. V. Gudim. His father Viktor Konstantinovich Vulf was a literature teacher at the 6th Warsaw Gymnasium. He grew up in Warsaw and graduated from the 6th Warsaw Gymnasium in 1880. He then went to the Imperial Warsaw University to study natural sciences. He studied under crystallographer A. E. Lagorio, and physicists N. G. Egorov and P. A. Zilov. In the third year, he studied the electrical properties of quartz for which he received a gold medal. In his fourth year he was assisting lectures of professor Zilov. He began to study the relationship of crystal structure and optical properties and in 1888 he published a paper on the "theory of rotatory polarization". He then went to St. Petersburg University working with E.S. Fedorov. In 1889 he went to Munich to study with Paul Heinrich von Groth. He also attended classes by Leonard Zonke. He also went to Paris and studied under Marie Alfred Cornu. While in Paris he married Vera Vasilyevna Yakunchikova. He returned to Warsaw to defend his master's thesis in 1892 on pseudosymmetric crystals. He then became a privatdozent at Warsaw University and lectured on mineralogy and crystallography. In 1897 he joined the Imperial Kazan University but returned to Warsaw in 1899. In 1907 he was invited to Moscow University by V. I. Vernadsky. He taught crystallography also at the Shanyavsky Moscow City People's University. He also collaborated with P. N. Lebedev. In 1911 he left Moscow University along with other professors in protest of Lev Casso. During World War I, Wulff helped develop new X-ray equipment. In 1917 he was restored to Moscow University and from 1922 he headed the Institute of Physics and Crystallography.