The world looked ahead Saturday to new American leadership, with U.S. allies and rivals alike starting to predict what the change in the White House would mean for their relations with the United States and for American engagement more generally. 

It did not take long after Joe Biden's victory was projected for world leaders to unleash the normal flood of congratulatory messages. But for those abroad who have felt uneasy with President Donald Trump and his norm-breaking style, it was a much-awaited moment of optimism and even jubilation.

Shouts of "Biden!" and cheers broke out in Berlin, London, Toronto and other cities when the excruciating wait for an announcement came to an end. On Twitter, echoing Paris' mayor, people tweeted out, "Welcome Back, America."

Many hope that Trump's unilateralism and America-first populism will give way to an era of renewed U.S. global leadership and an embrace of multilateralism to tackle common challenges.

"It's good that there are finally clear numbers. We look forward to working with the next U.S. administration," tweeted German Foreign Minister Heiko Maas. "We want to invest in cooperation for a transatlantic new beginning, a new deal.

Reinhard Bütikofer, a German member of European Parliament, quipped, "I heard a Pan-European sigh of relief, when Biden's victory was called."

Though Trump had yet to acknowledge his defeat, some of the foreign leaders closest to him did not delay in sending their congratulations to Biden and Vice President-elect Kamala Harris.

British Prime Minister Boris Johnson tweeted his congratulations., saying, "The U.S. is our most important ally and I look forward to working closely together on our shared priorities, from climate change to trade and security."

Poland's right-wing President Andrzej Duda, who has been has politically aligned with Trump, cautiously tweeted to congratulate Biden "for a successful presidential campaign." Egyptian President Abdel Fatah el-Sissi, whom Trump once called his "favorite dictator," sent his best wishes to Biden, and Indian Prime Minister Narendra Modi congratulated the president-elect. He also noted that Harris's Indian heritage is "a source of immense pride."

Harris's family hometown in southern India - the birthplace of her maternal grandfather - had already been holding celebrations in her honor ahead of the traditional Diwali festival. Meanwhile, Jamaica's prime minister, Andrew Holness, also saluted her family ties to Jamaica, the birthplace of her father, as well as her "monumental accomplishment for women."