If you consider Eastern Europe as being lands east of a line on the eastern borders of the Balkan states + poland + slovakia +hungary+ romania, then yes, somewhat he already controls it with the exception of Georgia (though I guess Georgia is Asian)
If you mean the former Soviet bloc, then no -- the Baltics, Poles, Hungarians, Romanians revile their time under Soviet rule
Still a lot of Russian ‘ 5th columnists’ inside these countries, esp. Estonia.
Putin is just reinstating a modified version of the “Brehznev Doctine”.
Look it up and you will have your eyes opens very wide.