The move should revive peace talks between the rebels and Colombia’s government that are being held in Cuba.
President Juan Manuel Santos had suspended two-year-old talks after the general, a captain and an attorney were seized in western Colombia on November 16.
The Revolutionary Armed Forces of Colombia said in a communique that it would release the three on Sunday to representatives of Cuba, Norway and the Red Cross, which are backing the peace talks.
The rebels earlier freed several other captives.
Mr Alzate is the first general to be taken by the rebel group in half a century of fighting.