From the Hebrew name יְהוֹשֻׁעַ (Yehoshu'a) meaning "Yahweh is salvation". As told in the Old Testament, Joshua was a companion of Moses. He went up Mount Sinai with Moses when he received the Ten Commandments from God, and later he was one of the twelve spies sent into Canaan. After Moses died Joshua succeeded him as leader of the Israelites and he led the conquest of Canaan. His original name was Hoshea.
The name Jesus comes from a Greek translation of the Aramaic short form יֵשׁוּעַ (Yeshu'a), which was the real name of Jesus. As an English name, Joshua has been in use since the Protestant Reformation.