The 20-year-old goalkeeper, who has German and American citizenship, has featured for USA Under-20s and previously played for college side the California Golden Bears.
He has been training with the Bundesliga club since last month and was informed on Tuesday by Hertha general manager Michael Preetz that he would be offered a deal.
Klinsmann's father, who was sacked as USA coach in November, has been a Hertha member since 2004, while his grandfather was a supporter of the club.
"This morning, Michael Preetz asked me to have a chat with him after breakfast," said Klinsmann. "He told me a decision had been taken regarding my contract with Hertha.
"It was an unbelievably emotional moment for me, because this club has so much history in my family.
"I’m looking forward to getting to know the club more, the city of Berlin and taking on new challenges in Germany."
Preetz added: "Jonathan convinced us with his ability, charisma and ambition. He'll now settle with us and develop step by step."
Klinsmann has represented the USA at the youth level 10 times and was the starter for the nation's first CONCACAF Championship at the U-20 level in March and was named the tournament's best goalkeeper. He followed that up by starting in the the USA's quarterfinal run at this summer's U-20 World Cup.
The keeper also drew the ire of fans of the USA national team in 2014, which he made a tweet seemingly mocking then-USA star Landon Donovan for not making Jurgen Klinsmann's final 23-man roster for the World Cup in Brazil.