The SCVO plans to use the money to train hundreds of charity workers as digital champions who will be able to help the people they work with make the most of the internet.
The cash will feed into a programme called One Digital, set up to support groups that might face barriers to accessing the internet, such as people with disabilities and accessibility needs, young adults seeking work and those over the age of 65.
Chris Yiu, director of digital participation at the SCVO, said: "This is an important step towards changing the lives of some of the million people in Scotland who lack the skills to get things done online."
Maureen McGinn, chair of the Big Lottery Fund Scotland, said: "Scotland’s third sector has a key role to play in building and sharing its digital experience with individuals and communities across Scotland."
She said the awards would "help develop this knowledge, while also creating digital champions to trial and test new approaches".