The 24-year-old, who has won 21 caps, becomes manager Alan Pardew's fifth signing of the summer.
Janmaat underwent a medical at St James' Park on Tuesday and arrives as a replacement for Mathieu Debuchy, who has completed his move to Arsenal.
"Daryl had an excellent World Cup and we're looking forward to him continuing that form for Newcastle," said Pardew.
Janmaat made five appearances at the 2014 Fifa World Cup in Brazil, where the Dutch finished in third place.
Pardew added: "He is the perfect example of a modern full-back.
"He is someone who is good defensively but offers a real threat going forward as well."
Janmaat made 63 appearances for Feyenoord over the past two seasons.
"This is the perfect club for me and I am looking forward to being with the team and getting started here."
He is the latest man to join Pardew's squad following the arrivals of Emmanuel Riviere,Remy Cabella,Siem de Jong,Jack Colback and Ayoze Perez.
Netherlands right-back Daryl Janmaat has joined Newcastle United for an undisclosed fee from Feyenoord.