Palestinian leaders say the work threatens Islamic archaeological remains and see the work as a huge provocation. Muslim leaders around the world have demanded all work on the site is halted.
Israel insists that the work poses no risk to the holy site.
The Temple Mount or Haram al-Sharif (Noble Sanctuary) is the holiest site in Judaism and Islam's third holiest shrine.
Live webcast
The Israeli Antiquities Authority says it wants to show that this is a proper archaeological dig.
"There will be three cameras in the excavation area. They will show a complete angle of the excavation area," Israel Antiquities Authority official Liat Eizenkot told AFP news agency.
Daily work at the site will be broadcast from 0630 local time (0430 GMT) to 1430 (1230 GMT), the Israel Antiquities Authority said.
The web camera would remain on outside working hours, she told AFP.
Broadcasts will start on Thursday and can be seen at the antiquities authority's website at www.antiquities.org.il/home_eng.asp.
A spokesman for the Islamic religious trust which runs the Haram al-Sharif said the new measures were just cosmetic action and that instead of putting up cameras, the digging should stop.
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The Haram al-Sharif is believed to be where the Prophet Muhammad made an ascent to heaven into the presence of God.
Jews believe the Temple Mount is where Abraham offered his son Isaac as a sacrifice to God and where Solomon built the First Jewish Temple.
Israel captured East Jerusalem in the 1967 war. Since then, the compound has remained under Muslim jurisdiction in conjunction with neighbouring Jordan.
