Grabbi was born on 22 September, 1929 in Tallinn.

In 1944, he fled together with his mother, grandmother and younger brother to Germany, and in 1949 immigrated to the US, where he earned a bachelor's degree in English and American literature and a master's degree in library science.

From 1955-1964, Grabbi worked as an editor for Vaba Eesti (Free Estonia) magazine, and from 1959-1967 worked at the Library of Congress, initially within the framework of the Free Europe Committee project.

From 1965-1999, he edited and published the magazine Mana, and he also promoted Estonian literature in the magazine Books Abroad/World Literature Today.

In 1968, Grabbi was a founding member of the Association for the Advancement of Baltic Studies (AABS). He also frequently featured on Radio Free Europe/Radio Liberty's Estonian-language programmes, appearing from 1975-1989 under the names of Kalju Põder and Toomas Rand to discuss politics and sports or literature, respectively.

He edited and published a number of books by Estonian authors, including Betti Alver, Ilmar Mikiver and Jaan Kross.

Since 2002, Grabbi began publishing chapters of his memories in Estonian magazines, publishing his first full memoir, "Child of the Republic," in 2008.

He was also an active member of the Estonian diaspora community in Washington and the US in general, serving on the boards of a number of diaspora Estonian organisations, and joined the Washington chapter of the fraternity korp! Rotalia in 1950.

Grabbi was bestowed the Order of the White Star, 3rd Class for his contributions to literature and culture and Order of the National Coat of Arms, 3rd Class for his service to the Republic of Estonia and the Estonian people.

He was also awarded the Cultural Award of the Republic of Estonia in 2012.