The full-back spent most of the last campaign with the Swans, but he left earlier this summer after he had failed to agree a new deal.
However, following recent talks between both parties, a compromise has been reached on a three-year contract.
"I'm very happy to have signed this contract. I had a great experience here last season and I'm delighted to be back," the Dutchman told the club's official website. "I know the people, the club, the stadium and the city. For me it's amazing to get back and to be part of Swansea City again.
"It took a little bit longer than expected to finalise, but my first thought was always to sign for Swansea. I played 25 games last season. That was a lot of games, more than I expected given the situation I was in last summer when I didn't have a club.
"I was very grateful to Swansea for the chance they gave me last season, especially to play in the Premier League - the best league in the world."
Tiendalli's form for Swansea last season earned him a call-up to the senior Netherlands squad.