Its chairman Stan Polovets said: “At great personal sacrifice, he fought for the rights and dignity of all ethnicities, religions and nationalities.
“Today, as we witness democratic principles being challenged and human rights, along with freedoms of thought and expression, denied to so many, Natan’s example is an inspiration to all those struggling for democracy.”
Mr Sharansky said he was humbled by the award.
“As my personal hero President Ronald Reagan said, freedom is never more than one generation away from extinction,” he said.
“It must be fought for, protected, and handed on for them to do the same, or one day we will spend our sunset years telling our children and our children’s children what it was once like to live when men were free.”
Mr Blair, the former British prime minister, said Mr Sharansky was a hero: “[his] courage united people all over the globe in a quest for freedom. He is a distinguished leader who made a significant contribution to the State of Israel, to the people who lived in oppressed societies of the Soviet bloc nations, and to humanity as a whole.”
Last year’s award was given to Robert Kraft, who owns the American football team the New England Patriots.
Previous winners of the Genesis Prize, which was launched in 2013, include Michael Bloomberg and Anish Kapoor.
Natalie Portman, the 2018 winner, refused to attend the prize ceremony in Jerusalem because she did not want to share a platform with Israeli Prime Minister Benjamin Netanyahu.
