The Scottish Gallery in Edinburgh, which has represented Morrison for more than 60 years, said there had been an "overwhelming response" from throughout the UK after "Eye of the Storm" was shown on the BBC Scotland channel and BBC Two earlier this month.
The film, which will now get a worldwide distribution, followed the late Montrose-based artist as he prepared to paint a final landscape as his eyesight failed him.
Filmed over two years by Scottish documentary maker Anthony Baxter, it painted a remarkable portrait of the artist just months before he died last year aged 88.
Widely regarded as one of Britain’s best contemporary landscape artists, Morrison captured the stormy seas and skies of his native Scotland as well as scenes from around the world including Africa, Canada, France and Arctic Greenland.
But while he was recognised by the art world - and collectors including the late Duke of Edinburgh - until now Morrison's was not an instantly recognised name among the general public.
Christina Jansen of Edinburgh’s Scottish Gallery, where Morrison held 25 solo exhibitions, said that screenings of Baxter's film had sparked an "unprecedented" reaction.
She said: "The response was phenomenal. Our website crashed due to traffic generated by the BBC2 screening, which is a first. There has been an overwhelming outpouring of emotional responses from all over the UK.
"It has been quite staggering. There were thousands of responses, all at once, from people who had connected with this artist or were touched by his life story.
"We've had up to 12,000 people looking (at Morrison's catalogues online). We have a lot of traffic on our website but that is extraordinary, and that is because of the interest generated by Anthony Baxter's very sensitive portrayal of Jim.
"As for his work, all of our publications have been wiped out and we have a very long queue of people wanting to acquire a James Morrison painting."
Morrison was born in Glasgow, and attended the Glasgow School of Art. He later moved to the north east of Scotland with his wife.
The Scottish Gallery has represented Morrison's work since 1959, and staged over 25 solo shows with the artist as well as contributing to exhibitions and art fairs worldwide.
The Gallery will hold a small studio exhibition live and online in September, looking at Morrison's career over the decades, which will include some works for sale.
A major memorial exhibition will then be staged in June 2022, showing work from Morrison's career from the 1950s up to his later work, including unseen work from his studio.
The Scottish Gallery will also work with Morrison's son, art historian John Morrison, to create a new hardback on the artist's life and work.
Ms Jansen said: "It is so lovely for us, through the power of Anthony Baxter's film, for Jim to have touched individuals right across the UK.
"We have always known that Jim is a spectacular talent and it is really great to see his work appreciated.
"More people are going to get to know Jim Morrison through a number of projects that we are going to do over the next couple of years. We are just sad that he is not here."
Morrison's work has previously fetched up to tens of thousands of pounds in the secondary market. Ms Jansen added that prices for Morrison's superb Scottish landscapes in particular could soar in value.
A theatrical length version of Eye of The Storm by Montrose Pictures - commissioned by BBC Scotland - premiered in a digital screening for the Glasgow Film Festival in March. It has also played at film festivals in Paris and Washington DC. Now a worldwide release of the film is planned through distributor Journeyman Pictures.
Film maker Baxter, best known for his acclaimed 2011 film, "You’ve Been Trumped" began filming with Morrison after the artist had turned 85. Troubled by the fact that -- on doctor’s orders -- he can no longer paint outside, he is also preparing for what would be his final solo exhibition.
Baxter said: "Perhaps after months of the Covid lockdown, there’s something about James’ breathtakingly beautiful landscapes that has struck a chord with the audience at this time."