The powerful 26-year-old arrives from Southern Kings, the South African club, and has touched down in Scotland just in time for Thursday's Heineken Cup squad registration deadline.
"Tomas is a physical, abrasive player, who is equally comfortable at No.8 or on the blindside flank," said Alan Solomons, Edinburgh's head coach who worked with Leonardi during his time as Southern Kings' director of rugby.
"He's an experienced international who is capable of adding value to the squad."
Raised at the prominent SIC club in Buenos Aires, Leonardi began his professional career in 2010 for Argentina's high performance squad, the Pampas XV, in South Africa's Vodacom Cup.
He went on to establish himself in the national side, earning 18 international caps to date, before joining the Kings franchise in 2013.