The 33-year-old former Birmingham City, Cowdenbeath and Hearts player joins the Bairns after leaving Dundee United last month.
McKinnon told the club website: “Morgaro is a really strong player in the middle of the park. He has played at a very good standard over the years and will be a real asset for us.”
The Ladbrokes League 1 club have also brought in midfielder Charlie Telfer from Morton as they continue to build for 2019/20.
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