The 16-year-old environmental activist is now on her way to New York and Chile to attend UN Climate Summits.
The Swedish teenager’s “school strikes” have inspired a global climate change protest movement driven by young people.
Fans gathered in Plymouth to wave her off on her voyage across the Atlantic.
The 16-year-old made a speech ahead of departing from Plymouth on the Malizia II, a solar-powered racing yacht with underwater turbines.
Greta said she was dedicated “to do everything I can” to tackle climate change which was a “very big problem”.
The teenager, who refuses to travel by air because of its environmental impact, said of climate sceptics: “There’s always going to be people who don’t understand or accept the united science, and I will just ignore them, as I’m only acting and communicating on the science.”
She added she thought people’s mindsets were changing “even if it’s not enough, and not fast enough, that’s something, it’s not for nothing”.
Greta was asked if she could make US President Donald Trump listen, and she answered with a simple “no”, prompting laughter from the crowd.
“I’m not that special. I can’t convince everyone,” she said.
“I’m just going to do what I want to do and what will have most impact.”
The captain of the Malizia II, Boris Herrmann, appeared alongside her. He thanked Greta for her courage and called the issue of climate change a “race against time”.
Greta said her two-week trip would pose challenges including seasickness, but said many people in the world were suffering a lot more than that.
“I was test sailing two days ago and we went out for several hours,” she said.
“I didn’t feel bad or anxious, I felt seasick for about one or two minutes, then it stopped.
“I will just have to see, get on the boat and and see what happens, and that is also very exciting.”
The 18m (60ft) yacht they are using was built to compete in the 2016-17 round-the-world Vendée Globe race.