Vekselberg said on Friday he was quitting TNK-BP but would remain a TNK-BP shareholder.
Slobodin will handle both TNK-BP's gas business and energy projects, a source close to TNK-BP was quoted as saying.
Slobodin, 38, has been in the electric power sector for 10 years and is new to the gas business. Gas production will become TNK-BP's key business, as it plans to boost gas output to 30 billion cubic metres by 2020, the paper said.
Vekselberg, who also controls IES Holding, one of Russia's leading electric power producers and suppliers, said he was quitting TNK-BP to focus entirely on Russia's Skolkovo hi-tech hub, the paper said.