The Weir Charitable Trust aims to support Scottish groups, individuals or other charities providing services in the country.
The Weirs scooped £161 million on the EuroMillions lottery in July 2011 - the largest jackpot won in Europe.
In a statement, they said: "We are delighted that the Weir Charitable Trust is now open for business. Since we won the EuroMillions lottery, it has been a privilege to be in a position to provide support where we could.
"But we have been looking at finding a more structured way to share our good fortune on an ongoing basis across Scotland. It has taken some time to set up, but we are pleased that the trust will now allow us to do that at a time when good causes in Scotland are struggling."
The trust will accept applications on a quarterly basis in five main areas - health, sport, culture, recreational facilities and animal welfare - for projects and activities that improve quality of life.
The first deadline for applications, available at www.weircharitabletrust.com, is March 7. Awards will be announced in early April.
Trust administration Lorraine Tait said: "There is no minimum sum to be applied for, we are more concerned that we reach groups, charities and individuals working hard in their communities, without mainstream support, who want to grow or who need funds to continue with their services.
"The main restriction is that the trust will only accept applications from Scottish-based groups or individuals, who will use the money in Scotland."