Jonty Claypole, head of arts for the BBC, who is based at Pacific Quay in Glasgow, said the four-part documentary would be broadcast next year in collaboration with the National Galleries of Scotland and he hoped the online festival broadcasts would be in place by this summer.
He said the BBC would be in discussions with directors of all the capital's summer festivals about broadcasting from their events, in what would represent a major increase in the corporation's coverage of the world-leading arts festivals.
Tony Hall, director general of the BBC, said the corporation's overall arts plans included the "strongest commitment to the arts in a generation".
The BBC is bringing in a series of "creative partners" to advise on its arts coverage, including Vicky Featherstone, the former director of the National Theatre of Scotland, who is now at the Royal Court in London. She said: "I would think that within a year or two years, you'd be able to feel a real significant change about the way that arts are talked about - how it's being democratised but not dumbed down.
"I think we're on the edge of looking to the future now."
Mr Hall said: "The arts are for everyone, and from now on BBC Arts will be at the very heart of what we do,"
Tate director Sir Nicholas Serota and National Theatre director Sir Nicholas Hytner are among leading arts figures being appointed to key consultation roles.