Kossak was born on 3rd October 1906 in Lviv. He finished the studies at the Faculty of Architecture at the Lviv Polytechnic in 1933. He was the son of Stefan Kossak, the director of Galicyjski Bank Krajowy (National Bank of Galicia), a nephew of a famous seaman, Wojciech Kossak, and Tadeusz Kossak, a major of the Polish Cavalry. His brother, Karol Kossak, continued the family tradition and took up painting. After finished his studies, he moved to Gdynia and became a partner of Zbigniew Kupiec. Together, they established an architectural design office Zbigniew Kupiec i Tadeusz Kossak inżynierowie architekci S.A.R.P which began operating in 1935.
He was the co-designer of many buildings, like the Franciscans’ St. Anthony Church in Gdynia, countess Łosiowa’s villa an 7 Korzeniowskiego Street, Adam Jurkowski’s tenement house in 16 Kościuszki Square, Marian Piotrowski’s villa in 1a Sieroszewskiego Street and the Kreński family’s tenement in 55 Świętojańska Street.
He received the 1st prize (together with Zbigniew Kupiec) for the plan of the Osiedle Armatorów estate in Gdynia and the Gdynia fire station.
After the World War II broke out in 1939, he was displaced from Gdynia and moved to Warsaw. After the war, he began working at the Warsaw Reconstruction Office. He was the main designer of the Mirów estate which is located in the Wola and Śródmieście districts. He was also the main architect during the reconstruction of the N-S road’s section running through the Mirów estate. It was presented during the first post-war exhibition on domestic architecture in 1953. He also worked for the Balneoprojekt company in Warsaw which provided hydrological services for health resorts.
In 1980, he received the Silver Badge of the Association of Polish Architects.
He died on 5th June 1984.