It follows the three-wheeled cycle rickshaws being trialled in Falkirk.
A video of volunteer rider Fraser Johnston taking the elderly on bike rides last year became an internet hit, notching up more than 28 million views.
Mr Johnston won a 2017 Pride of Britain Award for his work on the scheme with the Falkirk-based Communities Along the Carron Association.
The £300,000 Cycling Without Age (CWA) project, pioneered in Copenhagen in 2012, aims to help socially-isolated older people meet others and be physically active.
The new funding will see it expanded to East Lothian, Falkirk, the Highlands and Islands, Perth and Kinross, and the Borders this year.
These will be followed by further projects in Fife, South Ayrshire and West Lothian.
CWA Scotland executive officer Christine Bell said: “The act of two passengers sharing a trishaw, along with the volunteer pilots, creates new relationships and friendships, which has proven to be one of the most valuable aspects of this project.
“Elderly people are brought back into community life, stories are shared, and health and wellbeing improves for everyone involved.”
Care home resident Mary Duncan, 90, who was among the first to use the Falkirk scheme, said: “When I started going out it was marvellous - miraculous to just go on a bike.
“It was such a change to get out of the four walls.
“I really enjoy it - the fresh air and the wind in your hair. It’s just amazing.”
Fellow resident Jim Taylor, 96, who is unable to walk, said: “It eases the boredom quite a bit and there is a sense of freedom being out in the fresh air.”
Trishaw pilot Mr Johnston said: “You can see the positive impact it’s having on them.
“They have got the countryside around them and they actually create new memories, and that then stimulates a lot of conversations they would never have if they were sitting in the care home.
“It’s great for the volunteers - they have that one-hour adrenalin rush of sharing stories, and the memories they create with the passengers, and they are just desperate to get out again.”
Kirsty Peeblescorr, spokeswoman for CWA in Peebles, which is launching in July, said: “There are a lot of elderly people living independently who we are equally keen to reach.
“We will make use of the fantastic network of paths in Tweeddale.”
Public health minister Aileen Campbell, who announced the funding, said: “CWA started with the simple aim of helping older people feel the wind in their hair again.
“Through the committed action of a few volunteers, the project was brought to Scotland and has made a positive difference to many people’s lives.
“Through this funding, CWA will work with communities and partners to roll the project out across Scotland in the areas and settings where it will have the most impact.
“We know that physical activity and regular social interaction have huge benefits for both mental and physical well-being and help people in Scotland live longer, healthier lives.”