A dollop of glistening cream – complete with a cherry and a functioning drone – and a recreation of an ancient sculpture destroyed by Isis, will be the next artworks to sit on the fourth plinth in London’s Trafalgar Square.

Michael Rakowitz’s piece The Invisible Enemy Should Not Exist will occupy the plinth from 2018. The work is a response to what Rakowitz called the “cultural genocide”, and the accompanying human tragedy, happening in places such as Iraq and Syria.

Rakowitz’s towering work will reconstruct the sculpture of Lamassu, a winged bull, which stood at the entrance to the Nergal Gate of Nineveh in Iraq from 700BC until its destruction by Isis in 2015, along with other ancient artefacts in Mosul museum. It will take over from the current commission, a giant black thumbs-up, created by the British artist David Shrigley.

“It’s a real honour,” said Rakowitz, an American whose Iraqi grandparents fled the country in the 1940s. “[The plinth artwork] is happening at a time which is especially meaningful, considering the enormous number of people that are forced to leave Iraq and Syria and are seeking sanctuary. This piece becomes a kind of a placeholder for those human lives that can’t be reconstructed … whether it’s cultural genocide or the burning of books, it’s the destruction of artefacts that always accompanies a human catastrophe.”

The sculpture is part of a decade-long project by the sculptor to reconstruct ancient objects destroyed during or after the Iraq war of 2003, or more recently by Isis in Syria and Iraq. So far he and his team have recreated around 600 of the 7,000 objects missing from the National Museum of Iraq in Baghdad.

Heather Phillipson with a model of her work that will adorn the fourth plinth from 2020. Photograph: Dominic Lipinski/PA

“It’s devastating what’s happened,” he said. “Creating these apparitions of the originals has been a very meaningful work but it’s also become very clear to me how impossible it is to reconstruct history. Regardless of what our technologies are, the DNA of the societies can’t be put back together.”

Rakowitiz said London’s own multicultural fabric made it a very potent place to display the work, particularly somewhere as public as Trafalgar Square. The work will partly be created from empty cans of date syrup that are made in Iraq and he said he had visited Iraqi shops in London to begin to source the bottles.

“I visited the Edgware Road and went by these stores called Bagdad and Babylon Grocery and I recognised just how much of Iraq is here as well,” he said. “It’s one of the pleasures of being able to do a project in a place like this where there are different generations of Iraqis who left at different times.

“But it is also interesting to have it outdoors in a city that is part of a global discussion about immigration, a conversation that has been disappointing and vulgar.”

In 2020 the plinth will be given over to Heather Phillipson’s giant swirl of whipped cream, adorned precariously with a red cherry, a fly and a flashing drone, which will contain a camera surveilling Trafalgar Square 24 hours a day.

Phillipson said she was overwhelmed to be able to display work in such a “social and politicised context”, and said her sculpture reflected the congregational and celebratory aspect of Trafalgar Square as well as its political importance as a gathering spot for protest.

The flashing drone will be equipped with wifi that passersby can log into to see the drone’s view over Trafalgar Square on their phones. Phillipson said the drone element was a comment on how we had come to accept a surveillance society.

“I think my work exists somewhere in the realm of exuberant unease, so this is apparently very celebratory at first glance but the more time you spend time with it, other elements will start to creep in,” she said. “The plinth becomes a monument to hubris and impending collapse.”