A student of the Academy of Fine Arts from 1913, his masters were Tivadar Zemplényi, Ede Balló and Miklós Bottka. His studies were interrupted by the First World War, as he served in the military from 1915 to 1918. From 1919 he resumed his studies at the academy where his master was Ágost Benkhard. He attended the Graphics Department headed by Viktor Olgyai from 1922 to 1925 and worked as an assistant lecturer beside the master in the school year 1922-1923. His works were displayed in graphic art exhibitions in Budapest from 1923, and from then on he regularly participated in the exhibitions of the Association of Hungarian Etchers in Hungary and abroad. In 1926 his etchings were exhibited together with the works of Aba-Novák, Patkó and Szőnyi in the Hungarian Etching Workshop.

In the summer of 1926-1927 he worked in Igal, in the company of Aba-Novák and Patkó among others. In January 1927 his graphics and then in October his paintings could be seen in the Ernst Museum. He was awarded a graphic art prize named after Mihály Zichy of the Szinyei Merse Pál Society in the same year. In 1929 and then in 1932 again the Ernst Museum exhibited greater collections of his graphical pieces. He was awarded a bronze medal in the World Expo of Barcelona (1929), and a diploma of merit at the applied art exhibition in Monza. In the first half of the 1930ss his works were exhibited in the National Salon on two occasions (1931, 1934).

He Hungarianized his family name from Simkovics to Tarjáni in 1932, and from this year on he was referred to as Jenő Tarjáni and later as Jenő Tarjáni Simkovics. In the middle of this decade he designed clothes decorated with Hungarian motives and also ventured into the area of metal inlays and ceramics. He worked as a workshop leader at the Graphics Department of the Academy of Fine Arts from 1944 to 1954 side by side with Nándor Lajos Varga and then Károly Koffán. From the 1950s his works were on show in comprehensive history of graphics exhibitions. A selection of his graphic works were exhibited in the Dürer Gallery in 1965. In 1985 a recapitulative exhibition was held in the exhibition hall of the Academy of Fine Arts showing his drawings and etchings. During the 1990s his works could be viewed in a number of one-artist exhibitions, including one organised in the Erdős Renée House to celebrate his one hundredth birthday (1995) and another in the Csók Gallery (1995).