The 26-year old Dutch defender was bought in by the Swans boss as a free agent after regular left-back Neil Taylor was ruled out for the rest of the season with a broken ankle.
Despite having plenty of experience with the likes of Feyenoord, FC Utrecht and FC Twente, Tiendalli will not start at Aston Villa tomorrow with Laudrup preferring youngster Ben Davies on the left side of defence.
"Ben will play. He did great against Sunderland. But we needed a full-back because we need two players for each position," the manager said.
"We looked at other options but the most important thing was to find a player who was match fit. Dwight fits the bill."