Yair Klein was convicted in 2001 in absentia and sentenced to 10 years in prison for training far-right paramilitary groups in the South American country. He was also accused of working as a mercenary for Pablo Escobar's Medellin drug cartel in the 1980s.
Klein was detained at a Moscow airport last August after a tipoff from Interpol.
The court spokesman said Colombia had asked Russian authorities to detain and extradite Klein.
The Israeli Foreign Ministry on Tuesday strongly rejected criticism that not enough had been done to prevent Klein's extradition to Colombia.
It also said Foreign Minister Tzipi Livni had met her Russian counterpart Sergei Lavrov two months before and asked him to hand over Klein to Israel.
Klein lawyer, Mordehai Tzivin, is expected to appeal his client's extradition at Russia's Supreme Court.
