Bavarian Premier Markus Soeder announced the state would sign a precontract with a production firm in the town of Illertissen later on Wednesday.
Once the shot is authorized in the European Union, Bavaria would then receive the ordered doses, Soeder said.
Production in Illertissen could start this year, Bavaria's Health Minister Klaus Holetschek said. "It is a highly effective vaccine," Holetschek added.
The European Medicines Agency (EMA) is currently reviewing Sputnik V for authorization in the EU. EMA experts are expected to travel to Russia later in April to survey the production and storage of the jab.
Germany's vaccine roll-out has been slow amid difficulties with vaccine deliveries and supply.
First vaccine worldwide
Wolfgang Kubicki, deputy leader of the Liberal party (FDP), welcomed Soeder's move, saying he hoped it would bring some momentum to the campaign.
"With this, Soeder reveals the embarrassing slow-poking of the government's vaccine management," Kubicki said.
Russia already approved Sputnik V for use in August, the first vaccine against Covid-19 to be authorized worldwide, although medical trials had not been completed at that time.
In the meantime, data from the trials has been published and peer-reviewed, attesting to the shot's effectiveness.