Blatt, 55, most recently coached perennial Euroleague championship contender Maccabi Tel Aviv, where his team finished with a 54-18 record this season, winning the Israel League, Israeli Cup and the Euroleague Championship.
During his six years as head coach (2001-03 and 2010-2014), Blatt led the team to six Israeli Cup Championships and five Israeli League Championships. Over the past four seasons, Blatt's teams went 225-55, including a team-best 70-13 record in 2011-12.
Blatt also spent six years as head coach of the Russian National Team, where in 2007, he guided Russia to a FIBA European Championship over then reigning World Champion Spain in Madrid. During the 2012 London Olympics, he led Russia to the bronze medal, the only Russian basketball medal since the break-up of the Soviet Union.
"David is a great basketball coach and a special person," Griffin said in a statement. "His abilities to communicate, to build relationships with his players and to foster winning environments at several stops throughout Europe and across the highest levels of International competition speaks for itself.
"He brings unbridled passion, energy and creativity to his craft. These qualities have enabled David to reach a level of success that is truly unique.
"I have watched David's work for many years. He has an uncanny ability to adapt his system to maximize the talents of his teams year after year. That is why I am very confident he will make a smooth transition to the NBA."
Blatt played professionally in Europe from 1981-93, mostly in the Israeli League. After retiring from playing in 1993 with Maccabi Hadera, Blatt built a 20-year coaching career overseas, including head coaching stints in Israel, Greece, Russia and Turkey.
"David Blatt is going to bring some of the most innovative approaches found in professional basketball anywhere on the globe," majority owner Dan Gilbert said in a release. "Time and time again, from Russia to Israel and several other prominent head coaching jobs in between, David has done one thing: 'win'. He is not only an innovator, well-trained and focused on both sides of the court, but he is always learning and always teaching."
"I couldn't be more excited about the opportunity to come to Cleveland and lead the Cavaliers as their head coach," Blatt said in a statement. "After spending a great deal of time discussing the organization, the team and the head coach's role with David Griffin, I feel strongly about my fit for the job and this team's potential.
"This is an opportune time to join the Cleveland Cavaliers. We are going to work extremely hard to achieve the kind of results we all expect and know are possible."
A member of the gold medal winning USA National team in 1981, Blatt played point guard at Princeton under Basketball Hall of Famer Pete Carrill.
Blatt met with team officials for two days this week and was offered the job Thursday night, according to previous reports.