Under the initiative, the Scottish Government will offer 250 students bursary payments of up to £1750 and a student loan of up to £5500.
Students who currently study full-time abroad are only eligible for help with their tuition fees provided by the EU country where they are based.
Michael Russell, the Education Secretary, said officials would assess the demand for funding to ensure all Scottish students studying in the EU in future years would benefit. He said: "I want to ensure our young people have the opportunity to reap the cultural and career benefits of living and studying abroad.
"This pilot will help Scots studying at European universities and ensure money is not a disadvantage to students considering this option."
Stacey Devine, NUS Scotland women's officer, welcomed the announcement, saying it was "excellent news".
She said: "Studying abroad makes a huge difference to the lives, education and job prospects of those who take part, which is why the introduction of bursary and loan support for Scottish students studying at EU universities in 2014/15 is so important.
"We will also be looking for the Scottish Government to expand this pilot beyond 250 students."
The Scottish Government already provides funding towards Erasmus and other schemes to students at Scottish institutions who wish to study abroad for a year or a single semester.
This will be the first time Scottish students studying in Europe will be entitled to the same bursary and loan support as those attending university here.