The Soviet Union today officially announced the death Thursday of former premier Alexei N. Kosygin and said he would be buried at the Kremlin in Red Square, a place of honor reserved for revered Soviet leaders.

In announcing that Kosygin had died Dec. 18 "as a result of a sudden cardiac arrest," the official Tass press agency ended about 36 hours of official silence that followed the death of the 76-year-old former prime minister. Kosygin resigned from the leadership Oct. 23 after 16 years as the second most powerful man in the Kremlin.

It seems today that the delay in acknowledgeing his death was because yesterday was Soviet President Leonid Brezhnev's 74th birthday, when such nuews would have been inappropriate. The official obituary, according to Tass, contained rich praise of Kosygin and was signed by Brezhnev as well as "other party leaders and statesmen."

"Alexei Koysgin's utter devotion to the ideals of communism, selfless labor for the good of the Soviet state, modesty and tactful attitude to people won him a high prestige in the party and with the people," Tass said, quoting the obituary that will appear in all the country's newspapers Sunday.

Tass said the Communist Party Central Committee and the Council of Ministers "have decided to bury Alexei Kosygin on the Red Square near the Kremlin Wall." One of the last major figures buried at the foot of the wall was Klimenti Y. Voroshilov, a former Soviet president who was one of Stalin's closest comrades-in-larms. Stalin's body also lies at the foot of the Kremlin Wall, moved there from the Lenin Mausoleum one night during the height of Nikita Khrushchev's anti-Stalinist campaign.

Other important Soviet figures, such as politburo member Fyodor D. Kulakov , who died in 1978, are buried in the wall itself, their remains cremated and entombed in an urn behind a small granite stone. There has been speculation here that Kosygin's family might prefer his grave to be in Novodyeviche Cemetary, where his wife, Klavdia, is buried.

The government newspaper Izvestia, which carried a front page death notice and an obituary with a photograph of Kosygin on page three tonight, said the body would lie in state Monday at the Red Army Club. Burial is thus expected Tuesday.