Yakov, 78, teaches at US Princeton University and at the Landau Institute for Theoretical Physics in Moscow.
"Yakov Sinai is one of the most influential mathematicians of the twentieth century, the Norwegian academy said in a statement. "He has achieved numerous groundbreaking results in the theory of dynamical systems, in mathematical physics and in probability theory."
Crown Prince Haakon will hand Yakov the prize, worth six million kroner ($992,000) in Oslo on May 20.
The Abel prize was created by Norway's government in 2002 to mark the 200th anniversary of the birth of the great Norwegian mathematician Niels Henrik Abel, in order to make up for the absence of mathematics in the Nobel categories.