The unnamed man, who vanished in 2001, was found guilty of attempted murder and given a lengthy jail sentence.
The fugitive fled abroad and, according to police intelligence, spent many years in South Africa.
It was only when he turned up in Mexico, apparently for a visit, that he was arrested.
According to Israel Police, the convicted man shot and seriously wounded a father and son in the area of Carmel Market in Tel Aviv.
The shooting was apparently connected to the settling of scores in Israel's underworld.
The criminal, who shot the two men at close range, went underground after the assassination attempt and his trail disappeared.
He was subsequently arrested in Jerusalem disguised as an ultra-Orthodox Jew, and was apparently on the verge of fleeing to the United States with an American passport.
He was convicted and sentenced for the crime before successfully managing to escape.