Greenblatt is the son of Hungarian Jewish refugees, and grew up in Forest Hills, Queens, New York City. During World War II, his father fled Szatmárcseke in 1941 as a child, while his mother hid in Budapest with her family during the Nazi occupation, and fled to the United States after the Hungarian Revolution in 1956. He was born with the given name Theodore but had it legally changed as a teenager. He is the first cousin, once removed, of anti war Activist Robert Greenblatt.
Greenblatt started as real estate Lawyer for the New York law firm, Fried, Frank, Harris, Shriver & Jacobson. In the mid-1990s, he started a cappuccino coffee company, with pod machines at Penn Station and the New York City airports, but following the rise of Starbucks, sold his Business and returned to practicing law. Greenblatt is the creator of the blog Inspire Conversation, a collection of resources for parents and teens, as well as the author of three travel books, one about a family trip to Israel.
Greenblatt was educated at Yeshiva Dov Revel, the Marsha Stern Talmudical Academy, followed by Yeshiva University. In 1992, Greenblatt received a JD degree from the New York University School of Law.
Greenblatt has worked for Trump since 1997, rising to executive vice President and chief legal officer to Trump and the Trump Organization, and his advisor on Israel.
In late December 2016, Trump named Greenblatt as his Representative for International Negotiations for his incoming administration.
In May 2017 Greenblatt received an honorary doctorate (LL.D) from Touro College.