In the Bible, Eilat is known as Elath but the Bible also talks about Ezion Geber which was close to Elath. The location of these two sites is uncertain.
After 40 year of wandering, the Israelites turned north and travelled past the land of Edom. They turned from the Arabah road that runs from Elath and Ezion Geber and travelled the desert road of Moab. (Deut 2:8)
King Solomon builts ships at Ezion Geber, near Elath, which is described as being in the land of Moab. The ships sailed to Ophir and returned with gold. (1 Kings 9:26-28; 10:11-12; 2 Chron 8:17-18)
King Azariah rebuilt Elath and restored it to Judah. (2 Kings 14:21-22)
Rezin, king of Aram, captured Elath, driving out the people of Judah. (2 Kings 16:6; 2 Chron 26:2)