The scheme is one of several to be pursued as authorities seek to cut the 250 million visible bits of litter people drop each year and which is estimated to cost the country a minimum of £53 million a year.
Other moves outlined in the strategy — Towards a Litter-free Scotland — include imposing a 5p charge for single-use carrier bags from October this year and working with manufacturers to minimise waste packaging.
Details of the reward programme are yet to be worked out, but it would be available to communities for organising voluntary clean-ups in areas that are local litter blackspots.
Environment Secretary Richard Lochhead said: "Scotland is a beautiful country and we all have to play our part and take personal responsibility to keep it that way."
Iain Gulland, director of Zero Waste Scotland, said: "By reducing litter and fly-tipping and increasing recycling in public places, we can protect Scotland's natural beauty and harness the value of waste as a re-usable resource."
Derek Robertson, chief executive of Keep Scotland Beautiful, said they were "delighted that the Scottish Government has acted to give these issues a strategic focus".
He added: "To be effective, this strategy has to make a difference in the places where people live, work and spend their leisure, in our communities.
"Keep Scotland Beautiful will continue to work in partnership in communities throughout our beautiful country to ensure our shared objective of a cleaner and greener Scotland is delivered."