In a decree posted in an official database, Putin gave an order to "appoint Alexei Yerkhov as ... Ambassador of the Russian Federation to Turkey."
Yerkhov, 57, previously worked with Karlov as the Russian consul in Istanbul. He currently heads the foreign ministry's crisis centre which issues official travel advice.
Karlov, 62, was shot nine times at point-blank range by a 22-year-old policeman at the opening of a photo exhibition on December 19. He died on the spot.
The Turkish government blamed the murder on the group of US-based cleric Fethullah Gulen, on whom they also blame the failed coup attempt against President Recep Tayyip Erdogan last July.
More From This Section
Moscow has said it is too early to say who was behind the murder.
The street in Ankara where the Russian embassy is located has since been named after Karlov.
Turkey and Russia stand on opposite sides of the conflict in Syria as Moscow backs the government of Bashar al-Assad while Ankara supports the rebels.