The 20-year-old French winger made the move in a bid to get some first-team football under his belt.
"We've tried hard to get someone in to give us a few options and Leandre fits the bill," said Kevin Blackwell. "I'm pleased we could get him. He's a young winger who hasn't been getting an opportunity down there.
"He's got a lot of pace and can play on either the left or the right. He certainly gives us another option and is a welcome addition. His arrival could give us the opportunity to play David Healy in a more central role."
Griffit could make his debut in Saturday's FA Cup third-round tie against Birmingham City at St Andrews. He scored twice for the Saints last season and was Gordon Strachan's final signing at St Mary's.