Medvedev has also signed a decree for the government to resign in line with the Russian Constitution. However, the government will continue performing its duties until a new Cabinet is formed.
At least 226 votes are required to confirm the former president's appointment to premier.
The ruling pro-presidential United Russia party, which has 315 seats in parliament, the ultranationalist LDPR party and the Kremlin loyalist, A Just Russia party, with 40 and 38 votes, respectively, have already promised to support Putin. The Communist Party, which has 57 seats, announced on Tuesday that the probability that they would vote against was quite high.
If approved for the post of premier Putin will have to submit to the president proposals on the structure of federal executive bodies and candidatures for deputy prime ministers and federal ministers within a week.
Medvedev asked Putin to take up the premier's post last December on the condition that he was successful in the March 2 presidential polls. Putin agreed to accept the proposal after the votes had been counted. The lower house of parliament will consider his nomination on Thursday.
Later on Wednesday, Putin will hold consultations with the leaders of Duma factions and groups.
Putin will also become head of the ruling United Russia party, and analysts are at a loss as to how this 'power-sharing' will play out.