You have all the powers that Putin currently does. Everyone completely loyal to Putin is now loyal to you. Enemies of Putin are enemies of you. Putin no longer exists, and there has been a clean and absolute transfer of power to you. The economic, military, social and political situations are the same as they now are. You are not inhabiting Putin's body, you are just you. You're magically transferred to the Kremlin. The world at large doesn't know your past life, to them you have magically appeared as the new ruler. To everyone who knew you before, you just vanished.
Edit: no one knows your past life YET. They'll quickly figure it out. You will not lose any support based on your actions in your past life.
Reminds me of an 'elseworlds' Batman story from a while ago.
Bats kills R'as al Ghul but realizes that Ghul's evil empire is still operational. Batman takes the role of R'as, but sets it up so that all his top lieutenants take each other out. It takes a few years, but eventually the League of Assassins is a force for good in the world.
Something similar in Russia. Pit the worst of the worst against each other and let democracy prevail.
The idea is that they start with the characters in 1939 [when they premiered] and move forward decade by decade. Supes stays young while Lois gets older; Robin takes over from Bruce.