The 33-year-old has signed a two-year contract with the Scottish side.
Enckelman was a free agent after leaving Championship side Cardiff earlier this summer.
Enckelman featured for St Johnstone in the friendly against Real Valladolid on Saturday.
Enckelman said: “It’s been a whirlwind few days but it has gone well.
“I was surprised to play on Saturday after just one training session but I really enjoyed the game.”