The paper has a new look, while the editorial content is set to become more London-centric.
Since buying the title, Lebedev, who bought it through new company, Evening Standard Ltd, has taken an aggressive marketing approach.
As well as the free relaunch, which saw around 650,000 copies given away free, the title has introduced a staggered payment scheme, with the title available for as little as 10p depending on when and where it is bought.
In the last few weeks it has run an advertising campaign in which it apologised for the "predictability" and "complacency" of the title under its previous stewardship.
New editor Geordie Greig said on the paper's website yesterday: "Today is a new beginning for the London Evening Standard. You will see that we have put London into our front-page masthead — exactly where it belongs.
"It emphasises that we want to reach everyone who lives and works in the world's greatest and most vibrant city."
The newspaper goes up against both the London Lite, which is owned by DMGT, and News International's Thelondonpaper, both of which are free publications.
Evening Standard undergoes major relaunch
The Evening Standard relaunched yesterday following its acquisition by former KGB spy Alexander Lebedev in January.