The 26-year-old should go straight into Michael Laudrup's squad for the clash with Aston Villa on Saturday and says he's delighted to have joined the high-flying Swans.
"I am very happy to be here. It's a great opportunity for me to play in the Premier League for Swansea City," said Tiendalli.
"It's a beautiful club that plays good football and I love the way they play. I heard about Neil Taylor's injury and now I have to do my best every day in training to show people exactly what I can do.
"The only thing that makes me happy is playing football and I have been without a club so I am looking forward to playing football.
"This is a great opportunity for me. I'm so happy to be here."