Uzi was born in Jerusalem in January 1919 to Tova and Aviezer Yellin, a sixth-generation resident of the Land of Israel, and the grandson of the legendary David Yellin, one of the founders of the Hebrew Language Committee and the Israel Teachers Union, as well as a member of the Jewish National Council.

Uzi studied in the Rehavia Gymnasium, and he was one of the founders of the nationalist movement, Tzofei HaKehilla, which he headed. He was a member of Hagana Bet (Nationalist). As of 1937, he joined the IZL, which many members of Tzofei HaKehilla joined. He was an active member of IZL and a commander within the organization, carrying out retributive attacks against the Arab rioters during the 1936-1939 riots.

In 1938, he moved to Haifa to study architecture at the Technion, keeping up his IZL activities. When the split occurred, he joined Yair and became a Lehi member.

In Sukkot 1940, he married Sarah Lebstein (sister of Yaakov “Yashke” Eliav, one of the heads of Lehi), who was also a member of IZL and Lehi. Uzi was arrested in September 1940, a short time after Lehi attempted to seize money from the Anglo-Palestinian Company bank in Tel-Aviv, a failed attempt. The family succeeded in getting him freed, but after a short time, he was imprisoned again, for several months. In 1942, he was imprisoned, first in Mizra and then in Latrun, this time for more than a year-and-a-half. After considerable efforts, he was sentenced to house arrest, which meant that he could no longer participate in underground activities.

After the establishment of the State of Israel, Uzi enlisted in the IDF, serving as a secretary in Battalion 89 of the 8^th Brigade, throughout the War of Independence. Afterwards, he continued to serve, becoming the operations officer of the Commander-in-Chief of the Armored Corps. He held the rank of major. For many years, he continued studying via correspondence and became quite educated. In 1955, he returned to civilian life; he first worked for a private contractor, and then he started working for the Yovel-Gad Company, creating pipes for the National Water Carrier of Israel, where he first was director of manpower and then CEO of the company. Uzi became CEO of the Middle East Tube Co., Ltd. He stayed in this position for many years.

The Yellins had three children: the firstborn, David, born in 1942, died in the Yom Kippur War as a deputy battalion commander in the Armored Corps; the second, Azgad, was born in 1945; the third, a daughter, Diklah, was born in 1950.

Uzi passed away on 1.12.1988, and was buried in the Ariel-Barkan Cemetery.