Houston, 26, is understood to have attracted the attention of Bath coach Gary Gold while playing for Queensland Reds in 2011, prompting Gold to make a move.
Meanwhile, Orlandi, 29, has been a key performer in the past three seasons for Racing Metro.
Gold told the club's official website: "These are two very significant signings for Bath in that they say a lot about our ambition. Leroy is a guy I have admired for a long time, and we are delighted to have secured him. He's very dangerous with ball in hand, and loves to hit hard in defence.
"Juan Pablo is also a very powerful man. I spoke personally to the Pumas coach, Santiago Phelan, and he backed up our opinions, telling me that this guy is the real deal.
"To have depth in such key positions as tighthead prop is vital, and to add a world class player to our squad is very pleasing. We can't wait to get these guys training with us and to see them develop into Bath players."
Bath currently occupy seventh spot in the Aviva Premiership table.