"These memorials will be places where the family and friends of people killed in terrorist attacks can reflect and remember. By building them we are underlining our pledge to never forget the victims of these atrocities," Cameron said.
"An attack on British people anywhere in the world is an attack on us all. But these memorials will also stand as proof that we will not give up our way of life in the face of terrorism wherever it may be," he said.
A panel will be appointed to choose an artist and design for the tribute, which will be unveiled in summer 2017.
The public was asked to vote on a preferred site for the memorialafter the Prime Minister announced, in July last year, that a commemorative monument to honour victims of terrorist atrocities overseas would be built on British soil.
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The panel to be set up will have experience of commissioning art and now invite a small number of artists to submit proposals for the memorial, before selecting the final design.
The Prime Minister has also announced the launch of a consultation on a separate memorial to victims of attacks in Tunisia.
This consultation will be the first and most significant step in the process of formally seeking views from the affected families on the sort of location, look and feel of the memorial they would like to commemorate their loved ones.
The Sousse attack in Tunisia in 2015 was the worst incident of terrorism involving British citizens since the 7/7 attacks in London.
The National Memorial will be dedicated to all British victims of overseas terrorism and will stand to honour any future victims.