The 26-year-old Dutchman, who left FC Twente over the summer, has joined the Swans until the end of the season although the deal has yet to be ratified by the Premier League.
Tiendalli will provide defensive cover for Neil Taylor, who is expected to be sidelined for the rest of the campaign after fracturing his ankle against Sunderland 10 days ago.
"I'm looking forward to working under Michael Laudrup, who is a massive name in football, and showing him what I have to offer," Tiendalli said on www.swanseacity.net.
"Playing in the Premier League is something I have always wanted to do - it's the best league in the world.
"I know my opportunity comes after an unfortunate injury for Neil Taylor, but hopefully I can bring experience to the squad and more options for the manager.
"It would be great to play on Saturday against Aston Villa, but my concentration first and foremost is to impress the manager in training and get used to my new team-mates."
Tiendalli began his career with Ajax before moving on to spells with Utrecht, Feyenoord, Sparta Rotterdam and Twente.
- the Premier League