Capped 73 times by his nation, Mak arrives at the Sky Blues after back-to-back title-winning seasons in Hungary with Ferencvaros.
A Manchester City youth product, the 31-year-old has also played in Germany, Greece, Russia and Turkey during his career.
Slovakia's fourth-highest goalscorer, Mak was a member of his country's squad for the 2016 and 2020 Euros and has made over 30 appearances at club level in the UEFA Champions League and Europa League.
"I've been part of a few championships and cup wins in my career, so I know what it takes and want to bring my experience, personality and a few goals and assists to help us this season," Mak said in a statement.
Sydney are no strangers to Slovakian imports, with Karol Kisel and Filip Holosko having played for the club in the past.
Mak said conversations with both players convinced him to make the move to Australia.
"I am 100% determined to achieve the same success they achieved by also winning the premiership and championship double for this great club," he said.
Mak is the second signing for Sydney coach Steve Corica ahead of the new campaign as he revamps his squad after missing out on finals for the first time in six years.
Spanish full-back Diego Caballo was unveiled last month, with the Sky Blues having released several players including Kosta Barbarouses, Luciano Narsingh, Mustafa Amini and -- most controversially -- Milos Ninkovic.
"Robert is an excellent player. He has two great feet and can play on either side of the pitch," Corica said of new arrival Mak. "He likes to take on defenders and will create and score goals for us as well.
"To play that many times for your country is no mean feat and I think he will really stand out this season.
"It's a very good signing for us, we've taken our time to get him and there's more to come."