Born in London, Mehmet is of part English, Irish and Turkish Cypriot descent and has played for the Republic of Ireland U-21 team.
"I'm really happy and looking forward to playing with the club," Mehmet said.
At 1.89m, Mehmet is a tall, powerful striker who will add another dimension to Perth Glory's attack this season.
"Billy is a great acquisition," Perth Glory coach Ian Ferguson said.
"He gives us another option up front and compliments the forwards we have."
Previously, Mehmet has played for Dunfermline, St Mirren (both Scotland) and Genclerbirligi, Samsunspor in Turkey.
"Shane is a quality player and someone who scores a lot of goals, so hopefully, as a target man I get the chance to play alongside him," Mehmet added.
Already the signs are positive. On Saturday Smeltz scored two goals in a practice game against Football West Premier League side Bayswater with both goals created by Mehmet.
27 years old, Mehmet holds a few distinct records and says he hopes he can enjoy the Glory days in Perth.
- Mehmet was the youngest player to score in a first team match for West Ham at the age of 14 - He was signed by West Ham at 8 years old, and stayed with the club for 11 years. - He was the Youth team captain at West Ham.