Putin served two presidential terms in 2000-2008 before shifting into the prime minister's seat for four years to observe the term limit.
In resigning, "Medvedev said that, in view of the significant changes that will take place, he feels the president should be given the opportunity to go through with these changes through with the type of government that he chooses", Godfroid told Al Jazeera.
Putin has held a firm grip on the country since coming to power with Yeltsin's resignation in 1999, staying on as prime minister when Medvedev took the presidency.
Without much detail, Putin thanked Medvedev and his government for their work, TASS reported.
"Not everything was done, but everything never works out in full", Putin added. It is in the President's power to dismiss both the Prime Minister and cabinet ministers.More news: Whitney Houston, Notorious B.I.G. among Rock Hall inductees
"Yet, with Wednesday's speech suggesting the neutering of the presidency, Putin appeared to hint at wielding power through new constitutional architecture - perhaps as a newly empowered prime minister or member of an independent security council".
Russia's most prominent opposition leader, Alexey Navalny, quickly accused Mr. Putin - who has ruled Russian Federation as President or Prime Minister since August, 1999 - of trying to cling to power.
Medvedev's decision to step down after one term to let Putin return to the presidency also sparked massive protests in Moscow in 2011-2012 in a major challenge to the Kremlin.
Medvedev is a former Kremlin chief of staff who served under Putin until he was promoted to first deputy prime minister in 2005.
Earlier, Putin proposed sweeping changes to the constitution Wednesday, including strengthening parliament and revamping the country's state council, possibly hinting at his plans for after he leaves power in 2024.More news: Retired Lt. Gen. Michael Flynn Moves to Withdraw Guilty Plea
According to Putin, Russia is creating the world's largest archive of war-related documents to present the "truth" to the world.
It is the 16th time Putin has delivered the address before an audience that also includes government ministers, judges from the constitutional and supreme courts, leading regional officials, and other members of the political elite.
Putin also proposed that the State Council, now an advisory group to the president, be constitutionally enshrined with formal authority.
"This will increase the role and significance of the country's parliament". "People want development and are trying to make progress in the fields of vocation, knowledge, and well being", Putin said.More news: Trump is diverting another $ 7.2 billion to Pentagon funds for border wall