It was David Lloyd George who first described the first world war as "the deluge". In a speech to munitions workers on Christmas Day 1915 he acknowledged that the world crisis had become an earthquake, a convulsion of nature, which was unleashing forces that statesmen were powerless to control, much less to stop.

Fourteen months later, his words came true. The Russian Revolution of February 1917 set loose a terrible concatenation of events: the seizure of power by the Bolsheviks; Brest-Litovsk; the collapse of the Romanov, Hohenzollern, Habsburg and Ottoman empires; the Treaty of Versailles; the creation of new nation states in Europe and the Middle East; revolution and counter-revolution in central Europe; civil war and famine in Russia; the French occupation of the Rhineland in 1923, and the ensuing German hyperinflation. It was not until 1925 that some sort of order was restored – only then to be swept aside by the Great Depression and the Nazis.

Yet, of all the changes brought by the first world war, Adam Tooze argues in this bold and ambitious book, by far the most important was the arrival of the United States in a position of unparalleled economic, political and moral ascendancy. It wasn't simply that in 1916 America became the world's largest economy, she was also the war's banker. Wall Street paid for the battle of the Somme, and the US government bankrolled Passchendaele. By 1918 the US president, Woodrow Wilson, was in a position to dictate peace to the world; with, as its centrepiece, his idealistic plan for a League of Nations. Yet, when it came to assuming the role of world leader, America pulled back. Congress did not ratify the Peace Treaty; Washington did not join the League. The United States was not yet a mature enough democracy, Tooze argues, to assume her responsibilities. Fortunately, a generation later, under Roosevelt and Truman, she was.

So, was another war inevitable once Germany signed the Treaty of Versailles? Did allied insistence on reparations (and American insistence on the repayment of war debt) turn Weimar Germany into a failed state? Not necessarily, says Tooze; things might have worked out.

By the end of the 1920s, Europeans were on the way to restoring normality, with statesmen such as Gustav Stresemann in Germany and Aristide Briand in France patiently working towards the sort of understanding that would lead to the precursor to the European Union in the 1950s. In 1928, both Adolf Hitler and Leon Trotsky despaired that the capitalist order would ever be toppled, but the following year the crash on Wall Street detonated another chain of events, which sent Britain off the gold standard in 1931 and plunged Germany into economic and political chaos.

Some modern historians see interwar Europe as reverting to its dark past, rejecting democratic liberalism for autocracy and fascism; others treat this period as an interval between British and American world hegemony. Tooze rejects any idea of recidivism. To him, all the major nations of Europe and Asia were struggling to come to terms with modernity and modern geopolitics, groping their way towards a new structure of international security – yet ultimately tied to Washington's economic apron strings.

Within this overall structure he offers revisions and rewrites of the conventional narrative. His Woodrow Wilson is as much an American nationalist as a cloudy idealist; the French prime minister, Georges Clemenceau, was perfectly justified in seeking proper compensation at Versailles; the Washington Naval Treaty of 1922, not Versailles, set the seal on the new world of the United States' supremacy.

Tooze also makes skilful use of modern parallels and counterfactual scenarios – asking, for example, whether the determination of the allies to continue the war in 1917 killed outright the possibility of a democratic alternative to the Bolsheviks. He understands high finance and presents it with admirable clarity. Many of his statistics are spine-chilling: under the 1923 settlement of British war debt, London had to pay $4.6bn to the US at an interest rate of 3.3%. The annual payment of £162m was equivalent to the British national education budget.

The Deluge is the work of a fine historian at the peak of his powers, formidable in its range and command of the material, written in strong, muscular prose. It is also a demanding read – a long, dense, crowded narrative of diplomacy and high politics, in which policies, plans and politicians with unfamiliar names come relentlessly at the reader.

Tooze assumes reader-familiarity with the basic outline (both Stalin's rise to power and the Wall Street crash happen offstage) and the sheer momentum of events seldom allows space for analysis, anecdote or atmosphere. I kept making guilty, sustaining pit stops with Peacemakers, Margaret MacMillan's gossipy book about the Versailles conference, which is packed with the sort of human details Tooze doesn't bother with. More a sophisticated academic commentary than a narrative history, his book smoulders but does not catch fire.

Comparisons will inevitably be made with The Wages of Destruction, Tooze's masterly account of the Third Reich, which used the explanatory power of economic history to open new pathways. Here his approach is more conventional; ever since John Maynard Keynes wrote The Economic Consequences of the Peace the central narrative of the 1920s has always been economic. Nonetheless, this is probably the best of the current deluge of books about the first world war.

Ben Shephard's Headhunters: The Search for a Science of the Mind is published by Bodley Head on 12 June.