The winger, 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 the 25-year-old's 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 the 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."
Lamah, whose move is subject to Premier League clearance, will not be available for Wednesday's FA Cup third-round replay at Arsenal, but could be handed his debut in Saturday's league meeting with Stoke.
And he is eager to get down to work with Laudrup and a squad sitting in the top half of the Premier League and just 90 minutes away from a place in the Capital One Cup final.
He said: "To play in the Premier League is a dream, and also to play under Michael Laudrup is fantastic for me.
"I am looking forward to starting training and meeting the squad, and then I want to show everyone what I can do."
Chairman Huw Jenkins added: ""We've been watching him for a while.
"Michael has been looking to strengthen the wide positions to create more competition and we are delighted everything has been agreed."
