The memorial for those who died in the Normandy campaign will be unveiled in the French region on the 75th anniversary of D-Day in 2019.
It will have the names of the estimated 21,000 members of the British armed forces and Merchant Navy who died, as well as those from other nations.
The government's contribution comes from LIBOR fines levied on banks.
D-Day took place on 6 June 1944 and began the liberation of German-occupied north-western Europe.
BBC - iWonder - D-Day timeline- The beginning of the end of WW2
Prime Minister Theresa May said the memorial would be a "fitting tribute".
"Its unveiling on the 75th anniversary of the D-Day landings in 2019 will provide a timely reminder that we should never take our freedom for granted," she said.
A fundraising appeal will now be launched by the Normandy Memorial Trust, supported by the Royal British Legion, to add to the government's contribution.
The memorial will pay tribute to several thousand sailors and airmen who were lost at sea, and those who died from their wounds after being brought back to the UK for treatment.
It is hoped many of the remaining veterans, and the families of those who fought, will attend the unveiling ceremony planned for 6 June 2019.
George Batts, former national secretary of the Normandy Veterans' Association, said: "It has been the dream of Normandy veterans for many years for there to be a British memorial in Normandy dedicated to all those from the British armed forces who lost their lives in the D-Day landings and in the Normandy campaign which followed.
"This generous commitment by Her Majesty's Government will finally enable us to realise this ambition in time for the 75th anniversary of D-Day in June 2019."
Britons killed in the D-Day landings are to be remembered at a memorial the government is giving £20m towards.