Viktor Zubkov worked with Mr Putin in St Petersburg in the 1990s
Viktor Zubkov, head of the federal financial monitoring service, is a relative unknown in Russian politics.
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 Friday.
Mr Fradkov offered to resign earlier Wednesday, 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.
"We all have to think together how to build a structure of power so that it better corresponds to the pre-election period and prepares the country for the period after the presidential election in March," Mr Putin said in accepting Mr Fradkov's resignation.
Strong platform
Elections to the Duma are to be held in December.
VIKTOR ZUBKOV 1941: Born in Arbat village, Sverdlovsk region 1965: Graduates from Leningrad Agricultural Institute in economics 1967-1985: Works on collective farms in Leningrad regions 1985-1991: Works in regional administration 1991-1993: Works with Vladimir Putin in St Petersburg city administration 1993-2000: Works for federal tax service and tax ministry From 2001: Head of financial monitoring service
Profile: Viktor Zubkov
Whoever becomes the new prime minister gains a strong platform from which to campaign to replace Mr Putin, correspondents say.
Russian media had been speculating that First Deputy Prime Minister Sergei Ivanov - long considered a frontrunner for the presidency - could have been about to be made prime minister.
Mr Ivanov worked under Mr Putin in the FSB, the internal intelligence agency, in the 1990s and the two men are believed to be close.
Power struggle?
Mr Zubkov's links with Mr Putin go back to the early 1990s, when he was the future president's deputy on the St Petersburg city external relations committee.
But few in Russia believe that Mr Zubkov is now in the running for the presidency, says the BBC's Rupert Wingfield-Hayes in Moscow.
Instead, says our correspondent, many analysts believe he has been appointed to ensure a smooth transition between Mr Putin and his successor, whoever that might be.
Mr Ivanov is one of President Putin's closest allies
Dmitry Medvedev, the other first deputy prime minister, has also been seen as a possible presidential candidate.
The choice of Mr Zubkov suggests a behind-the-scenes power struggle between "clans" within the Kremlin that are differentiated mainly by their degree of hostility toward the West, says the BBC's Russia analyst Steven Eke.
White House National Security Council spokesman Gordon Johndroe said the choice of leaders was a matter for the people of Russia to decide and that the US "looks forward to continuing its good relations with the Russian government".
Mikhail FradkovImage Credit:Ricardo Stuckert/PR
Prime Minister of Russia Mikhail Fradkov has resigned, citing his reason as being "the approaching major political events in the country and a desire to give the president full freedom in making decisions, including personnel." Russian President Vladimir Putin has nominated Victor Zubkov to replace him, and a new cabinet is expected to follow as well.

Parliamentary elections are expected to take place in three months as the parliament has not been dissolved, and presidential elections will take place in six months.