Despite having only a 1.7 per cent chance of obtaining the first selection with the ninth-best odds, the Cavaliers emerged as victors in the much anticipated lottery.
In 2011, Cleveland finished with the second-worst record in the league but earned the right to pick point guard Kyrie Irving of Duke with the top selection.
Last year, the Cavaliers had the third-best chance of scooping the lottery, yet still came out on top and chose forward Anthony Bennett of the University of Nevada, Las Vegas.
Australian Irving, a twice NBA All-Star, was delighted by Tuesday's lottery news and tweeted: "Luck of the ping pong balls...Very exciting!!!"
The Milwaukee Bucks, who ended up with the league's worst record in 2013-14, will pick second in this year's draft, followed by the Philadelphia 76ers, who endured a 26-game losing streak during the regular season.
The next 11 lottery picks will be made by the Orlando Magic, Utah Jazz, Boston Celtics, Los Angeles Lakers, Sacramento Kings, Charlotte Hornets, 76ers, Denver Nuggets, Magic, Minnesota Timberwolves and the Phoenix Suns.
The Lakers, in the lottery for the first time since 2005, dropped one spot in the order to seventh while the Celtics, looking for their first lottery win, slipped one spot to sixth.
The top picks in this year's draft are expected to include players such as Andrew Wiggins and Joel Embiid from Kansas, Jabari Parker from Duke and Australia's Dante Exum.
The 2014 NBA Draft will be held in Brooklyn on June 26.
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