Swans have paid £2m to land Stamenic.
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The New Zealand international, 23, has agreed a four-year deal with the option of a further 12 months.
Stamenic spent part of last season on-loan with Olympiakos.
"We've been talking about this move for some time now. I've been told about the plans and the project and I fell in love with it from that first meeting," Stamenic said.
"I am just over the moon that the deal is done."