The Invisible Enemy Should Not Exist by Michael Rakowitz is one of two commissions announced for the central London square's Fourth Plinth.
The other artwork is THE END by Heather Phillipson, a sculpture portraying a whirl of cream topped with a cherry, parasites and a drone
The works will be unveiled in 2018 and 2020.
The Invisible Enemy Should Not Exist is a project begun by Rakowitz in 2006 that attempts to recreate over 7,000 archaeological artefacts looted from the Iraq Museum during the war or destroyed in its aftermath.
For the Fourth Plinth the artist will recreate the Lamassu, a winged bull and protective god that stood at the entrance to Nergal Gate of Nineveh from 700BC.
In 2015 it was destroyed by so-called IS along with other artefacts in Mosul Museum.
It will be made of empty Iraqi date syrup cans, representative of a once-renowned industry decimated by the Iraq wars.
The Fourth Plinth Commission described THE END as exploring "the extremes of shared experience, from commemorations and celebrations to mass protests, all while being observed by a drone's camera".
Ekow Eshun, Chair of the Fourth Plinth Commissioning Group said: "I wish to congratulate Michael Rakowitz and Heather Phillipson on winning the commission.
"Their works are wondrous, striking and deeply engaging.
"The new commissions will proudly continue the legacy of the Fourth Plinth in putting world-class contemporary sculpture at the heart of London."
The current artwork, David Shrigley's Really Good, will be displayed on the plinth until March 2018 when it will be replaced by The Invisible Enemy Should Not Exist.
THE END will be displayed in 2020.
A recreation of a sculpture destroyed by so-called Islamic State (IS) is to be displayed in Trafalgar Square.