The world, Blair said, was at a turning point in history comparable with the end of World War Two or the collapse of the Soviet Union: but this time the West is clearly not in the ascendant.
"We are coming to the end of Western political and economic dominance," Blair said in a lecture entitled "After Ukraine, What Lessons Now for Western Leadership?" according to a text of the speech to a forum supporting the alliance between the United States and Europe at Ditchley Park west of London.
"The world is going to be at least bi-polar and possibly multi-polar," Blair said. "The biggest geo-political change of this century will come from China not Russia."
Russia's invasion of Ukraine has killed thousands and triggered the most serious crisis in relations between Russia and the West since the 1962 Cuban Missile Crisis, when many people feared the world was on the brink of nuclear war.
President Vladimir Putin says the West has declared economic war by trying to isolate Russia's economy with sanctions and the Kremlin says Russia will turn to powers such as China and India.
The war in Ukraine, Blair said, had clarified that the West could not rely on China "to behave in the way we would consider rational".
Chinese President Xi Jinping has continued supporting Putin and criticised sanctions "abuse" by the West. Putin has forged what he calls a "strategic partnership" with China.
China in 1979 had an economy that was smaller than Italy’s, but after opening to foreign investment and introducing market reforms it has become the world’s second-largest economy.
Its economy is forecast to overtake the United States within a decade and it leads in some 21st century technologies such as artificial intelligence, regenerative medicine and conductive polymers.
"China’s place as a superpower is natural and justified. It is not the Soviet Union," said Blair, who was prime minister from 1997 to 2007. Its allies are likely to be Russia and Iran.
The West should not let China overtake militarily, he said.
"We should increase defence spending and maintain military superiority," Blair said. The United States and its allies "should be superior enough to cater for any eventuality or type of conflict and in all areas."