The 25-year-old, who can play on either flank, is manager Michael Laudrup's first acquisition of the January transfer window and Swansea have the option of making his switch a permanent one at any time during his loan spell.
Ivory Coast-born Lamah, who also has top-flight experience in Belgium, Holland and France, told Swansea's official club website: "This is a great opportunity for me and I'm happy to be here.
"I know a few of the players here, and I already know that Swansea is a family club that will suit my style of play."
Swans boss Michael Laudrup hailed his new signing's versatility, stating it was key to his capture.
"He is a player we had already watched before the season started," admitted Laudrup.
"He is a player who is not a forward but who can play behind the striker in all three roles.
"He has a lot of individual quality, he is quite strong and has good quality one against one as well as a good shot.
"He is a player that can be very useful for us. We saw when Pablo (Hernandez) was out for four weeks and Wayne Routledge was out as well, we missed that we didn't have players in positions with those characteristics, that's why I think it's good for us he's here.
"He has not played that much this season, Osasuna are struggling but are a strong team, but I think that he will have a chance here and I am looking forward to working with him."