Speaking to an audience in Brighton, a seaside town on the south coast of England, Sanders praised Corbyn's willingness to address issues such as wealth inequality, poverty and class.
"Too many people run away from ... the grotesque levels of income and wealth inequality that exist in the United States, that exist in the UK, and exist all over the world," he said.
"Globalization has left far too many people behind," he said. "The wealthiest people on this planet, regardless of where they live, are doing phenomenally well, while at the same time workers all over the world are seeing a decline in their standard of living."
He likened Corbyn's rejection of mainstream politics to his own.
"What has impressed me -- and there is a real similarity between what he has done and what I have done -- he has taken on the establishment of the Labour party and gone to the grassroots. And he has tried to transform that party and take on a lot of establishment opposition.
"That is exactly what's taking place in the United States and what I'm trying to do with the Democratic Party," he continued.
As part of his three-day trip to England, he continued the theme Friday in a speech to students at The Cambridge Union Society.
"At the end of the day, if we are going to create governments that work for all of us, if we are going to deal with healthcare and create great educational systems and protect the environment and combat climate change, and deal with issues like women's rights and gay rights and combating racism, we need to have a government of what Abraham Lincoln described... of the people, by the people and for the people, and not a government of billionaires and large multinational corporations."
He added, "So I applaud Corbyn for raising those issues, which I think are important for my country, for the UK and for every major country on earth."
Tyler Shores, an American PhD student at the University of Cambridge, attended the event Friday. He'd voted for Bernie Sanders in the California Democratic primary last June, but had never seen him speak live.
"Sanders was dynamic," he told CNN. "He has a very electrifying presence... And there is a similar energy in Corbyn."
And the similarities don't end there.
As well as focusing on class and income inequality, both men are campaigning for systems of healthcare and education that are available to all, regardless of income, and condemn the tax evasion practiced by some multinational corporations.
Moreover, one of Corbyn's key pledges is to raise the minimum wage to £10 an hour (around $13) by 2020, while Sanders would like to see a minimum hourly rate of $15 in the United States.
Both men also want to make college and university tuition-free.
David Graeber, a professor of anthropology at the London School of Economics, also sees parallels in the way that the two men and their left-wing policies -- which are often very popular among voters -- have been presented in some of the mainstream media.
Sanders and Corbyn were "considered a joke" and "treated as crazy for holding to positions that the majority of people actually agree with," he told CNN. Both were made to seem "unelectable," he said.
But as support grew for Sanders during his campaign for the Democratic presidential nomination and as Corbyn and his party have narrowed the gap with Theresa May's Conservative Party in the run-up to the UK election, Graeber saw this change.
With the chance to speak directly to voters, Sanders and Corbyn began to gain support and momentum, particularly among young people.
"They come across as decent, honest human beings," said Graeber. "I don't think it's occurred to most young people that a politician could be an honest person."
And they've reintroduced the idea "that politics can be transformative," an idea that Graeber thought had been lost. "Young people no longer thought of politics as about changing the world," he said. "The trick is to try to convince people that it can work."
"Polling suggests that the brand of left-wing populism that Corbyn represents could have broad appeal and translate to an electoral surge," she wrote, "similar to the surprise grassroots support for Bernie Sanders in the United States."
Like Sanders, who defied predictions by winning popular support, "Corbyn won the the leadership of his party (and fought off a second challenge a year later) by winning huge grassroots support from party members."
Whether Corbyn will defy predictions of a Conservative landslide and win the election next week is another matter, however.
"These may be popular policies, but elections are also about leadership and whether voters believe someone can do a good job leading the country," wrote Merrick. "Even Corbyn's own circle will admit that Sanders... failed to seal the deal."
Sanders seems more confident that his British counterpart could succeed. Asked by an audience member in Brighton what advice he would offer to Corbyn, he responded: "I don't think Jeremy Corbyn needs my advice. I think he's doing quite well, nor do I think the people of the UK need my advice on who to vote for."
Sanders' other stops include Oxford, where he spoke Friday afternoon, and London. He'll be appearing at the Hay-on-Wye literary festival on Saturday.