Mr Zubkov is head of the federal financial monitoring service.
The change marks a major political shake-up ahead of parliamentary and presidential elections.
The lower house of the Russian parliament, the Duma, is set to vote on Mr Zubkov's nomination on September 14.
Mr Fradkov offered to resign earlier on September 12, citing “approaching significant political events”, said Itar-Tass news agency.
Mr Putin asked Mr Fradkov to stay on as acting prime minister until his replacement is confirmed.
Elections to the Duma are to be held in December. None of
Dmitry Medvedev, the other first deputy prime minister, has also been seen as a possible presidential candidate.
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