"We will soon become the principal shareholder of Svyaz Bank," VEB chairman Vladimir Dmitriyev said. "At the final stage of negotiations with current shareholders we have agreed on a symbolic sum of 5,000 rubles in return for 98% of the bank's stock."
Russia's Federal Anti-Monopoly Service has already approved the takeover, he said.
However, the Central Bank has yet to sign off on the deal.
Dmitriyev said less than a quarter of Svyaz Bank's 90 billion ruble ($3.5 billion) loan portfolio was seen as high-risk, mostly corporate loans.
This is the first big bailout involving a retail bank since the Russian financial sector was hit by the global credit crunch.
Svyaz Bank, which has 49 branches across Russia, was downgraded by Moody's on long-term global local and foreign currency deposit ratings from B2 to Caa2 and on its bank financial strength rating from E+ to E.
The Russian government said in late September it would lend Svyaz Bank $2.5 billion to stabilize the struggling lender and enable it to meet its obligations.
Analysts say problems with liquidity experienced by the Russian banking sector could trigger a wave of consolidations, and reduce the number of lending institutions in Russia by a third.