"There's a big, dark cloud hanging over Portugal. (…) There is no real future for my generation," Almeida told CNBC.

Instead, she bought a ticket to Dili, the capital of East Timor. Two weeks after she arrived she found a job as a communication consultant in a museum in East Timor.

"I found hope in East Timor," she said. "I don't want to go back to Portugal any time soon."

Almeida is just one of many citizens from debt-choked European countries moving overseas, particularly to former colonies, in search of a better future.

As youth unemployment in Europe continues to rise, young Spaniards are leaving for Latin America and Miami in the U.S., where the Spanish speaking community outnumbers English speakers; Portuguese are heading to Brazil, Angola and East Timor; and young Irish and Greeks are opting for Australia, which has large diaspora communities from these two countries.

(read more: Euro Zone Unemployment Hits New High, Inflation Eases)

Numbers from Europe's statistics agency captures the migration that is under way.

The number of 20- to 29-year-olds fell by 8.8 percent year-on-year in Ireland, by 4.3 percent in Spain and by 3.5 percent in Portugal in the second quarter of 2012, according to Eurostat data.

Earlier this year, Laszlo Andor, the European Employment Commissioner, also called on unemployed youth in the European Union to consider opportunities across the border: "If we want to create more opportunities for the young people, we have to create and highlight … opportunities in other countries."

Compared to 2009, the number of short-term arrivals of Greek citizens in Australia are up 21 percent to about 4,000 people between May and November 2011, according to Australia's statistics bureau.

Numbers from Ireland's Central Statistics office in April showed that more than 3,000 Irish are leaving the country each month, the highest number since the famine between 1845 and 1852. According to the Economic and Social Research Institute, net emigration out of Ireland is expected to be 100,000 over 2011 and 2012, with Australia listed as the primary destination.

Portuguese Prime Minister Pedro Passos Coelho last year expressed his desperation about the situation in his country, and said that the only solution to soaring youth unemployment was for the 'lost generation', as the young are increasingly called, to emigrate.

He suggested they to go to "Angola, and not just Angola," and highlighted the great teaching void in Brazil.

The Portuguese seem to be following up on that advice as the government reported that the Portuguese population in Brazil increased 20 percent between 2010 and 2011.

On the other hand, Brazilians themselves no longer seek better opportunities abroad, the numbers show. From 2005 to 2010, the number of Brazilians living abroad dropped from an estimated 4 million to 2 million as a result of Brazil's booming economy, according to the country's Ministry of Justice.

The number of Spaniards emigrating to Latin America in 2011 stood at a rough 370,000, about 10 times more than before the economy started to tank in 2008, according to Reuters.

(read more: Reversal of Fortunes Sends Spaniards to Latin America)

"Spain is losing an entire generation," Alexis Cogul LLeonart, a 30-year old Spanish architect, told CNBC.

LLeonart set up his own architecture firm in Spain in 2008, but soon after Spain's housing crisis hit.

"In less than 6 months, 9 out of 10 projects I was working on were put on hold. All clients were sending the same message: 'We don't know what is going to happen so we have to wait and we can't pay now'," Lleonart said.

As it became clear that the situation in Spain was "more about survival than about opportunity," Lleonart said he couldn't choose the professional goals he wanted to pursue. So he packed his bags and moved to Miami, Florida, where he is now setting up a new firm Cogal Architecture.

Although he is still working around the clock as he was doing in Spain, he is hopeful. "In the U.S. I can actually pursue opportunities and grow as an architect, something that wasn't possible in Spain," he said.

—By CNBC.com's Liza Jansen; Follow Her on Twitter @lizajansen