Sobyanin, who has been a top aide to Prime Minister Vladimir Putin since 2005, was seen as the front-runner from the list of candidates the ruling United Russia party submitted to Medvedev for consideration. He must now be approved by the Moscow City Duma, a step widely viewed as a formality.
Russian television showed Medvedev giving Sobyanin the news during a meeting at the president's residence in Gorki outside Moscow.
"I have decided to submit your candidacy for the post of mayor of Moscow to the Moscow City Duma," Medvedev said. "I'm sure that this job is very difficult and very important and that you can handle it."
Sobyanin took up the challenge with enthusiasm.
“This is a big responsibility and big sign of trust [in me]," he said. "I will try my best to justify being given this mandate."
"There has really been a lot done [in Moscow] in the last years, but at the same time, there are serious issues which demand immediate solutions,” Sobyanin added.
The 52-year-old is set to replace Yury Luzhkov, who was fired by Medvedev on September 28 after 18 years in office.
Luzhkov transformed Moscow from a bleak Soviet capital into a bustling international metropolis that now accounts for a quarter of the Russian economy.
Prickly and independent-minded, he frequently clashed with successive Russian leaders over his nearly two decades in office, and was one of the last remaining power bases in the country not under the direct control of the Kremlin.
But Luzhkov was also mired in corruption allegations and he drew particularly harsh criticism for his handling of the smog that plagued the city during wildfires in August.
After a long standoff with Medvedev, the president fired Luzhkov, saying he had "lost the president's confidence." Before he was sacked, Luzhkov was targeted in a series of muckraking documentaries on Russian television exposing corruption in the capital.
Unlike Luzhkov, Sobyanin enjoys close ties with Russia's ruling tandem of Medvedev and Prime Minister Vladimir Putin. He is widely expected to be more pliant and to steer a less independent path than his predecessor.
Sergei Mitrokhin, the chairman of the opposition Yabloko party, said that in picking Sobyanin, the Kremlin made sure to choose someone who is “highly dependable.”
If confirmed, the appointment would bring tighter Kremlin control over the massive financial and business empire the outgoing mayor built in the capital.
Medvedev asked Sobyanin to "make Moscow's economic life more open, more competitive, and based on the law." He also instructed him to focus on fighting corruption.
"One of these [problems facing Moscow], which we should talk about candidly and openly, is corruption," Medvedev said. "Unfortunately, little has been done [to curb corruption] in recent times. And in some cases we have seen schemes that raise questions, at the very least, about their legality."
Sobyanin was born in 1958 in the village of Nyaksimvol in Siberia's energy-rich Khanty-Mansiisk Autonomous District. He worked his way up through the administrative ranks in the town of Kogalym, where he worked with Vagit Alekperov, who would later become CEO of the oil company LUKoil.
He served as mayor of Kogalym in 1991-93 and later as governor of the oil-rich Tyumen Oblast in 2001-05.
In 2005, Putin, then the president, brought Sobyanin to Moscow to serve as his chief of staff. Sobyanin also headed Medvedev's 2008 presidential campaign.
Since 2008, when Putin left the presidency to become prime minister, Sobyanin has served as deputy prime minister.
Despite his political experience, the Kremlin’s decision to back Sobyanin for Moscow mayor was met by skepticism on the part of opposition politicians, some of whom questioned Sobyanin’s familiarity with the city’s unique needs.
For his part, Sobyanin said, "This is not the first year that I am living in Moscow and I know the troubles and problems of the city well."
Yabloko leader Mitrokhin predicted he could face trouble winning the confidence of Muscovites as a non-native of the city.
Other opposition politicians said the choice of Sobyanin was not the real problem, as much as the top-down selection process which dominates most levels of Russian politics.
"I don't see an opportunity to support by means of a vote any of the candidates that were offered, " said Andrei Klychkov, the leader of the Communist faction in the Moscow city Duma, in an interview with RFE/RL's Russian service.
"Then again, in this particular case, I wouldn't like it to look like I'm not providing support for Sobyanin. I'm not ready to support any person under this system that deprives us of the opportunity to elect directly," he said.
The Kremlin scrapped direct election of regional governors, along with the mayors of St. Petersburg and Moscow, under Putin in 2004.
with agency reports and contributions from RFE/RL's Russian Service