Jüssi was born on Aruba, where his father worked for a Venezuelan oil company. His family returned to Estonia and settled in Tallinn when Jüssi was 3 years old. After finishing high school in Tallinn he studied biology and zoology in Tartu University, graduating in 1958. He has worked as a school teacher (from 1958 to 1960 in Emmaste, Hiiumaa), as inspector for nature protection (1962–1975), radio broadcaster for Eesti Raadio, freelance writer and nature campaigner. In Eesti Raadio he ran the program Looduse aabits (ABC book of nature) from 1976 to 1986. In the beginning of the 1990s he was for a few years the president of Estonian Nature Fund. Jüssi has published numerous books, articles and audio recordings related to nature. He was the first recipient of Eerik Kumari Award, given to him in 1989.
Jüssi is probably the most influential person in Estonia engaged in writing, talking and popularising nature.