Was Caleb a foreigner, even though he represented the tribe of Judah (Numbers 13:6) and was one of the first judges of Israel (Judges 1)? In Numbers 32:12 and Joshua 14:14 we read that Caleb is the son of Jephunneh the Kenizzite. And in Genesis 15:19 we read that the Kenizzites were some of the original inhabitants of the land promised to Abraham. Also, the name "Caleb" means "dog," a term used for foreigners (according to the BDB Hebrew lexicon).
Divrei Hayomim 2:18 says that Caleb was the son of Chetzron. Radak there says that this is Caleb ben Yefune. Radak says he was known as ben Yefune since he turned away from the Meraglim's blasphemy of the land.
Ibn Ezra disagrees and says his father's name was Yefune and his grandfather's name was Kenaz.
Rashi (Numbers 32:12) says that Calev is called "Kenizite" after his stepfather Kenaz (so "the Kenizzite" refers to him, not to Yefuneh). And I Chronicles 4:15 (thanks @DoubleAA) says he had a grandson named Kenaz (or maybe Ukenaz), probably named after his stepfather.
There were provisions for a Gentile to be included in Israel as were clearly spelt out in the regulations for Passover (Exodus 12: 48,49). Some consider Kenizzites as an Edomite tribe, in which case Caleb would be a descendent of Jacob´s brother Esau.
But many view Caleb as a true Israelite by birth, since he is associated with and represented the tribe of Judah as one of the 12 spies. Jephunneh could have descended from some member of the non-Israelite Kenizzites (Ge 15:18, 19) who associated with the descendants of Jacob (Israel), marrying an Israelite wife. Perhaps the name Kenizzite in his case derives from some ancestral Judean family head named Kenaz, even as Caleb’s brother was so named (Joshua 15:17; Judges 1:13; 1 Chronicles 4:13).