The move was announced in a decree (in Russian), in which Mr Putin also ordered trade talks with Turkey.
The ban on charter flights hurt the tourist industry in Turkey, a favourite destination for many Russians.
The Kremlin accepted a letter from Turkish President Recep Tayyip Erdogan as an apology this week.
Mr Putin spoke to Mr Erdogan by phone on Wednesday, telling him he planned to lift the travel sanctions.
The lifting of non-travel trade sanctions will depend on the outcome of the trade talks, the Russian leader said in his decree.
Mr Putin also condemned Tuesday's gun and bomb attack on Istanbul's Ataturk airport, one of the busiest in the world.
Mr Erdogan had expressed "regret" earlier this week to Mr Putin and to the family of the Russian pilot killed in the incident.
The fighter jet was shot down near the Syria-Turkey border in November. Turkey said the jet had been warned repeatedly after entering Turkish airspace, a claim fiercely denied by Russian officials.
Mr Putin said he had been stabbed in the back and accused Mr Erdogan of collaborating with so-called Islamic State.
Russia responding by hitting Turkey with a raft of sanctions, stopping the Russian package holidays and banning the import of Turkish foodstuffs.
The Russian Su-24, an all-weather attack aircraft, was flying in skies above the Turkey-Syria border area on 24 November when it was shot down by Turkish F-16s.
The plane crashed in the mountainous Jabal Turkmen area of the Syrian province of Latakia, killing the pilot.
A Russian marine involved in a helicopter rescue attempt was killed when the helicopter came under fire from local fighters.
The navigator in the jet, Capt Konstantin Murakhtin, survived the crash and was taken to Russia's Hmeimim airbase in Latakia by Syrian government forces.
Turkey said planes were warned 10 times during five minutes via an "emergency" channel and asked to change direction.
The Russian defence ministry insisted that the aircraft remained within Syria's borders throughout its mission and did not violate Turkish airspace and received no warnings.
Russian President Vladimir Putin has lifted curbs on tour firms selling holidays in Turkey, brought in after a Russian jet was downed last year.