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A statement late this evening said: "Our forces have now completed the liquidation of the German Fascist troops encircled in the area of Stalingrad.
"The last centre of enemy resistance in the Stalingrad area has thus been crushed."
The declaration brings to an end five months of heavy fighting for the city. The battle has been described as among the most terrible of the war so far.
Another 45,000 German soldiers have been taken prisoner in the last two days, bringing the total in custody to over 90,000 officers and men.
The prisoners are understood to be in an appalling condition after enduring months of starvation in temperatures down to -30°C.
They are the remains of the 330,000-strong German force sent to take Stalingrad.
The rest - about a quarter of a million men - have died, as many from illness, starvation and frostbite as from the fighting itself.
The 6th Army has been trapped inside the city, completely surrounded by the Red Army, for almost three months during the harshest part of the Russian winter.
They have had to rely totally on air drops by the Luftwaffe for food.
Atrocious weather conditions have reduced the amount getting through to just 90 tonnes a day - less than a third of what they needed.
The German commander of the 6th Army, Field-Marshal Friedrich Paulus, gave himself up two days ago.
He had been in a hopeless position since early December, when a last-ditch rescue attempt was driven back by Soviet troops.
He was given one earlier chance to surrender, on 8 January, by Soviet Regional Commander, Marshal Rokossovsky.
But Hitler repeated his order to the 6th Army that surrender would not be contemplated, and two days later the final Soviet offensive began to flush the Germans out of Stalingrad.
Paulus lost his last German-controlled airfield ten days later, on 22 January, and with it the last hope of any more regular supplies.
By 29 January the desperately weak 6th Army was split into two pockets of men.
The surrender of Field-Marshal Paulus brought the ordeal to an end for one of the groups.
The defeat of the second remnant today closes at last one of the most horrific chapters of the war so far.
The Germans attack on Stalingrad began on 19 August 1942.
Stalingrad was a strategically important city in their campaign to occupy the south of Russia and take control of the Caucasus oilfields.
It was also of symbolic importance as the city named after the Russian leader, Joseph Stalin.
The Red Army fought from inside the city, forcing the German soldiers into intense, house-to-house urban warfare under heavy shellfire from the German army and its allies surrounding the city.
Then on 19 November 1942, a massive force including three entire Soviet armies counter-attacked from outside the city.
Two more Soviet armies attacked the following day, 20 November.
They smashed the German siege and encircled Stalingrad themselves, trapping 300,000 soldiers of the 6th Army inside.
The defeat at Stalingrad threw Hitler's offensive in the Soviet Union into disarray, and was a turning point in the war in Europe.
It was also one of the bloodiest battles in modern history.
Nobody knows exactly how many people died at Stalingrad.
On the German side, estimates put the number of dead from the 6th Army and its allies at about 300,000.
The Soviet government never released accurate figures. A conservative estimate is that at least 500,000 Red Army soldiers died in the fighting.
Civilian casualties are thought to have been even higher.
The population of Stalingrad - now Volgograd - fell from 850,000 to just 1,500 at the end of the war.
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