All over 18s who have not yet received an appointment will be contacted by phone or letter, with the first vaccinations due to take place on Saturday.
Moray has seen a rapid rise in cases recently, with 95 cases per 100,000 population, by far the highest rate in the country.
An incident management team set up to try to bring the virus back under control has urged people to get tested even if they do not have symptoms. Door-to-door testing is being “heavily considered” for Elgin, the epicentre of the outbreak.
The situation is being “closely monitored” by the Scottish Government after warnings from local health chiefs that Moray may not be able to move to level two Covid-19 restrictions with the rest of the country as planned on May 17.
Moray Police told locals to “stick to the current covid guidelines”, announcing community police patrols over the weekend in areas which have seen reports of young people gathering.
The acceleration of the vaccine programme means NHS Grampian expects all adults in Moray to receive a first dose ahead of the July 31 target for the rest of the country. A new target date for the local area has not yet been set.
The Scottish Government said NHS Grampian had been able to draw vaccine from stocks used to smooth out delays to vaccine delivery, and that the additional amount is enough to vaccinate almost all under 40s in Moray.
The health board said the increased appointments will not affect the vaccine delivery to over 40s currently underway.
A health board spokesperson said: "NHS Grampian plans delivery of its programme to maximise the use of stock it receives. In other words, the pace of the vaccine programme is defined by the stock we receive.
"Unexpected additions to stock, which matches the needs of Moray's under 40 population, can be delivered with no impact on our other planned vaccination of the 40–49-year-olds, and can be done quickly to help suppress the virus in Moray, meant the decision was made to allocate these vaccines to Moray as part of the response to the concerning increase in Covid-19 transmission.
"Telephone calls are already being made to offer appointments to those aged 18-39 years in Moray and the first appointments for this age group will take place tomorrow (Saturday 8 May).
"We hope to have offered first dose appointments to everyone in this age group in advance of the national target which is the end of July."
Katrina Morrison, NHS Grampian vaccination clinical lead nurse, said: “Additional Covid-19 Pfizer vaccination stock and the concerning, uncontrolled, sustained community transmission of Covid-19 in Moray has made this decision straightforward. It needs to happen quickly and our staff have been mobilised to speed up the process.”
A Scottish Government spokesperson said: “Our ambition remains that the country will be able to move together in the easing of restrictions however the Scottish Government is working with the National Incident Management Team to closely monitor the situation in Moray and ensure that any decisions best support the progress that has been made in reducing the prevalence and impact of the virus.”