The Foxes confirmed last week that they had reached an agreement to sign Soyuncu from Freiburg, but the Turkish centre-back has needed to wait for a work permit to be issued.
Puel has confirmed that all the necessary paperwork has been processed, but says that the 22-year-old will not feature against Wolverhampton Wanderers on Saturday afternoon.
At a press conference, Puel told reporters: "It's official. He's a Leicester player. We are happy to wish him a good welcome. He arrived tonight and will not be fit for this game.
"After a little injury he will come back into training."
Soyuncu could be considered for a debut against Southampton on August 25.