The 28 year-old Nasoko made his international sevens debut in 2016 and was named in the World Series dream team in his first two seasons on the circuit.
He was appointed captain of the Fiji sevens team in December and will join his new club in the summer following the completion of the current sevens series campaign, which resumes next month in Hong Kong.
"I'm very excited by the opportunity to join Edinburgh. I am friends with Viliame Mata and he has said great things about the club - I can't wait to get started," he said.
"This is a great opportunity for my family, and after many years on the Sevens circuit, I can't wait for this new challenge in Scotland. Everyone sounds very welcoming and I am looking forward to running out in front of the Edinburgh fans."
Edinburgh head coach Richard Cockerill, added: "Kalione is a tremendously exciting player who is obviously captain of the Fiji Sevens side. He'll predominantly play as a winger, but he has also played at 13.
"Kalione brings something different to our back-three. He gives us a little bit more of an x-factor and, as you see with the good teams around Europe, you need that type of threat."
Eroni Sau was also included in the Sevens World Series dream team last season and named the best newcomer in his debut campaign before signing with French side Perpignan.
The 29 year-old scored a hat-trick on his Flying Fijians test debut against Uruguay in November and also featured in the historic victory over France a week later.
"I'm really excited by the opportunity to join Edinburgh and to test myself in the Guinness PRO14 and in Europe too," he said.
"After speaking with Richard Cockerill and my friend Viliame Mata, I knew it would be a great move for my rugby career and also for my family. I can't wait to work hard in the summer to earn a place in the team next year."
Richard Cockerill added: "Anyone who has watched sevens will know Eroni Sau. He's a very strong and powerful runner, he's tough and very combative.
"A nickname like 'The Sledgehammer" gives you an idea of what he does with and without the ball, and I'm delighted he's chosen to join Edinburgh and be part of what we're building here for next season and beyond."