He studied at the Tallinn Technical University from 1947 to 1949, and graduated from Leningrad University in 1952. Rebane received a PhD in Solid State Theory in 1955 from the Leningrad (St. Petersburg) University and a Doctor of Science degree in Theoretical Physics in 1964 from the Institute of Physics of the Belarusian AS at Minsk. He joined Tartu University in 1955 where he held both teaching and administrative positions, including Professor and Chair of the Experimental Physics Department (1958–60), and Professor and Chair of the Joint Department of Laser Optics at the Institute of Physics and Tartu University (1974-1993). He was president of the Estonian Academy of Sciences from 1973 to 1990.
- 2006 - Order of the White Star Class III
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