Klein was freed from a Moscow jail where he was held on a request by the Colombian government which wanted him extradited on charges of training right-wing militias.
"Klein has been freed and he is currently en route to Israel," Interfax news agency quoted the Russian security source as saying on condition of anonymity. He declined to provide any further details.
Israeli television Channel 2 also reported the release and showed video of a smiling Klein leaving his prison in Moscow before heading to the airport and his flight back home.
According to the TV report, Klein said the first thing he wanted to do is see his family and criticized Israel for not obtaining his release sooner.
In 2001, a Colombian court sentenced the 67-year-old Klein in absentia to 10 years and eight months prison for training death squads who waged war against the Colombian state in the late 1980s and early 1990s.
Klein, a former colonel in Israel's parachute infantry, was arrested in Moscow in 2007 under an Interpol warrant where he went for a holiday and for business.
He had been detained for 16 months in the West African country Sierra Leone between 1999 and 2000. He was accused of selling arms, training Liberian rebels and trafficking diamonds.
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