The work had been in a Scottish private collection since the 1920s, but was allocated to the gallery through the Government’s Acceptance in Lieu scheme.
And on Sunday it went on display to the public.
The piece features the limestone cliffs on the Normandy coast, which were a common subject in Monet’s works.
Etretat, L’Aigulle et La Porte d’Aval was produced around 1885 at Etretat, famous for its rock formations such as the Porte D’Aval and the Needle, which are featured in this pastel.
Sir John Leighton, Director-General, National Galleries of Scotland, said: “This is the first work on paper by the outstanding French Impressionist Claude Monet to enter the national collection.
“It provides a wonderful complement to the major paintings in oil by the artist already in Edinburgh and is an atmospheric composition of remarkable subtlety and interest.
“We are immensely grateful to everyone who has made possible its transference to public ownership through the AIL (Acceptance in Lieu of Tax) scheme.”
Fiona Hyslop, Cabinet Secretary for Culture, Tourism and External Affairs, said: “This Monet is a distinguished addition to the Scottish National Gallery.
“The Acceptance in Lieu scheme is a fantastic system that allows galleries and museums to be allocated important pieces for the public to enjoy, and I look forward to seeing this outstanding pastel piece in its new permanent home in Scotland.”
The Monet piece was owned by a Valerie Middleton who opted to gift it to the public using the Acceptance in Lieu scheme.
The scheme enables taxpayers to transfer important works of art and other heritage objects into public ownership while paying Inheritance Tax.
If an offer is accepted, the taxpayer is given the full open market value of the item.
In this case, the amount settled on was £700,000.