Goel was born on June 15, 1920 to Yitzhak and Hannah Ozeri. Goel had two brothers and three sisters. In 1936, he joined the Nationalist Hagana (what would become the IZL), staying until the split in 1940, when the connection with him was lost.
In 1942, Avraham Tehomi, who had been the commander of the Nationalist Hagana, approached him for a special mission: since Goel was fluent in Arabic and could pass for an Arab, he was charged with finding two more young men like him to gather intelligence in Beirut. This activity was coordinated with the Free French in Lebanon, and they were in contact with their representative in Beirut, Maurice Fischer. However, after three weeks, their contact told them that the British suspected them of being fugitives from prisons in the Land of Israel. After a conformation with a senior British officer, the testimony of a Jewish police officer from Israel and the testimony of a cabdriver cleared up the error, but this also meant the end of their mission. Between 1942 and 1944, Goel served in the British Navy on and off, until he met Geula Cohen in 1944 and he returned to active duty with Lehi. He remained in the Land of Israel for the rest of his life.
He was part of all continuing operations, taking courses and going out on missions, including: laying mines on roads to attack military vehicles, leaving an explosive device on the railroad, confiscating money and diamonds in the polishing center at Pardes Katz and the Exchange on Lilienblum Street, robbing Bank Discount on Yehuda HaLevi Street and Barclays Bank on Allenby Street, blowing up Naaman Bridge, blowing up the Intelligence building in the alley by Jaffa Street, Tel Aviv (in which Major Duran was killed), attacking the Kfar Syrkin Airfield (in which nine RAF Spitfires were blown up, among others).
In the IDF, he served in the Israeli Navy, as chief of the engine room.
In 1950, Goel married Margalit Levi (a Lehi member herself), and they had three children: Eitan (Avigdor) in 1951, Orit in 1954 and Galia in 1959.
After the State was establsiehd, Goel worked for four years for ZIM; later, he worked in an office at the Tel Aviv-Jaffa Municipality, until he retired in 1985 at 65.