The documents state that the Luhansk, Donetsk, Zaporizhzhia, and Kherson areas have been "admitted into the Russian Federation."
However, Ukraine claimed it has been retaking more villages in two of those regions—Luhansk and Kherson.
In addition, Mr. Putin authorized the formalization of Russia's takeover of the Zaporizhzhia nuclear power station.
The Russian president signed agreements with the four presidents of the regions that Moscow had appointed during a formal event that took place in the Kremlin last Friday.
The action followed what the West referred to as "sham" self-proclaimed referendums in the regions.
However, the situation on the ground seems to be different, with Ukrainian forces advancing in both the south and the east.
The BBC was informed on Wednesday by Serhiy Haidai, the Ukrainian governor of Luhansk, that six villages in the area had been retaken.
Later, according to President Zelensky, Ukraine had liberated three more villages in Kherson's southern district.
That came after other victories in Kherson the day before, including the important strategic hamlet of Davydiv Brid.
A few hours before morning, a series of enormous explosions shook the southern city of Zaporizhzhia.
According to local authorities, seven Russian missiles hit residential buildings, and people are reportedly buried beneath the debris. As of yet, there is no information about casualties.
Rescuers are searching through the shattered remnants of a beautiful five-story apartment building in the centre of the city, according to Paul Adams of the BBC who is at the area.
According to Dmitry Peskov, the spokesman for the Kremlin, Russia would reclaim any area it had given up to Ukrainian forces.
In response to inquiries about the recent losses, he said to reporters: "There is no inconsistency in this. They will be given back and remain in Russia forever."
On Russian Teachers' Day, Mr. Putin gave an address to educators in which he promised to "calmly advance" the annexations.
The head of the State Duma defense committee, Andrey Kartopolov, however, told state media that Russia needed to stop lying about what was happening on the battlefield and that Russians were not naive.
As a result of Mr. Putin's announcement last month that 300,000 people who had finished their conscription would be called up, Russia is still attempting to mobilize reservists.However, Mr. Putin has backtracked on which categories will be impacted in response to vocal opposition and demonstrations in Russia.
He has issued a directive exempting a number of student groups, including first-time enrollees at recognized schools and specific postgraduate students, such those studying science.
In a separate development, President Putin has signed a document formalizing Russia's seizure of the nuclear power plant in one of the districts it has seized, Zaporizhzhia, which has been held by Russian forces since the beginning of the conflict.
Russia claims that a new business would run the plant, which is the biggest nuclear facility in Europe, but Ukraine's nuclear operator has called the announcement "worthless."
IAEA Administrator Rafael Grossi has stated that he will hold talks with both sides in the wake of this development. The IAEA is the UN's nuclear watchdog.
In order to create a protection zone around the facility, which is located close to the front lines of combat, he is traveling to Kyiv and then Moscow.
BBC
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