Capped 18 times by his country, the 26-year-old back row has made five starts in seven appearances including four games in the RaboDirect PRO12.
And after securing his long-term future, Leonardi intends to continue his progression in the Scottish capital.
"This is great news for me. I've worked really hard in my time here and I'm really happy to re-sign for the rest of this season and one more," said Leonardi.
"When I first came here I was really impressed with the facilities, the squad and the coaching, so was very excited to get the opportunity to train and play.
"In these three months I've done my absolute best to perform for the club and make a good impression.
"Securing a longer deal eases my mind a bit and allows me to focus more on myself and plan some longer-term improvements for my game, but I'll still work as hard, day by day, to repay the coaches for the faith they've shown in me."
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