Depending on whether their asylum requests are recognised, the Syrians will either be ultimately returned to Austria or deported from the EU, Slovak interior ministry spokeswoman Michaela Paulenova told AFP.
The 18 men were transferred by bus from Austria's Salzburg to a temporary asylum camp in Gabcikovo, a southwestern Slovak village of 5,400 people.
Five hundred asylum-seekers are to be temporarily accommodated in Gabcikovo under the agreement with Vienna.
"This number will be reached in the following two years. We have no information on how many asylum-seekers and when they will arrive. It's up to the Austrian interior ministry," Paulenova said.
Gabickovo held a referendum last month in which 97 percent of voters rejected the temporary asylum camp, but the interior ministry "is not obliged to act according to its results", Paulenova said.
Getting off the bus on Thursday, one asylum-seeker thanked "all the good people" for the possibility of staying in Slovakia, local media reported.
But villager reaction on social media was cold.
"Who wants them here anyway? I know I don't," Gabcikovo resident Beata Lelkes wrote on Facebook.
"Many homeless here would appreciate accommodation like they (migrants) are getting," resident Zsuzsanna Varga added.
The nation of 5.4 million people is among several eastern EU members staunchly against a system of fixed quotas proposed by the European Commission to distribute 160,000 refugees among the bloc's 28 members.
On Wednesday, leftist Prime Minister Robert Fico alleged the EU was no longer safe and raised the spectre of terrorists entering Slovakia under the guise of refugees, a possibility experts deem unlikely.