Yehoshua was born on July 28, 1921 in Rozyszcze, Poland to Yisrael and Yona Becker. He studied in the Tarbut Hebrew school and joined Beitar at a young age. Right before the Germans invaded Poland, he made aliyah, in April 1939, settling in Kfar Saba, where he worked in agriculture. In 1940, after the split in IZL, he joined Lehi to fight the British. He was placed in the operations division, under the command of Yehoshua Cohen. In memory of his father, Yehoshua changed his last name to Yisraeli.
In 1942, he was involved in an operation to seize cash for the underground, which ended in armed pursuit and an exchange of fire. Yehoshua was captured, tried and sentenced to death. His interrogation involved severe beatings by the British officers. For 45 days, he sat on death row, until his sentence was commuted to life imprisonment. He started serving his time in Jerusalem Central Prison but was soon moved to Acre Prison. On April 4,1947, IZL organized a prison break, and Yehoshua was free for the first time in five-and-a-half years. He returned to active duty, taking a course in advanced weaponry and going out on combat missions. He was put in charge of the southern district, then Samaria. He put mines on the roads used by British Army caravans, derailed a British Army train near Zikhron Yaakov, and took part in the operation to abduct three Hagana members and keep them in a shack in Zikhron Yaakov, in retribution for the abduction of three Lehi members by the Hagana.
After the announcement of the Partition Plan and the outbreak of hostilities with the Arabs, he moved to Jerusalem and joined Lehi forces there under the command of Yehoshua “Meir” Zattler, at the Dror camp in Talbiyeh. As Meir’s lieutenant, he was part of the attempt to liberate the Old City. In September 1948, after the Bernadotte assassination, as Lehi members were being arrested all over the country, he went underground and took charge of the Tel Aviv district, until the general clemency was announced in February 1949. At that point, he joined the IDF, serving in the Israeli Navy.
Yehoshua opened a business to fix typewriters and accounting machines, travelling to the United States on business. When he returned to Israel, he expanded and set up a company for accounting machines, which he ran. In 1950, he married Rachel Lviev; they had two daughters and numerous grandchildren. In 1989, the family moved to Karnei Shomeron.