The documentary is being shown today on state TV, marking a year since the widely questioned referendum in Crimea that supported its secession from Ukraine.
The referendum was held about three weeks after Yanukovych fled the Ukrainian capital after months of street protests that turned increasingly violent. He eventually turned up in Russia, but details of his movement had not been known.
Putin says in the documentary that Russian security forces had tried to keep contact with Yanukovych as he moved through Ukraine and eventually "we brought him to Russian territory."