The Scottish government has invested £10m in the pilot, which has been tested in the Highlands, Western and Northern Isles, Moray, and Argyll and Bute for the past year.
As it extends to the west of the country, participating bus operators will be reimbursed by public body Transport Scotland.
Swinney said bus travel was the most widely used form of public transport in Scotland and the government was working to make it “as affordable, accessible and attractive as possible”.
He said: “This is vital to grow the economy, travel sustainably and protect the planet.”
First Bus, one of the bigger bus companies operating across Glasgow, Dumbarton, Kirkintilloch and Lanarkshire, said it would continue to work with the government to ensure the cap was a success.
But just days before the start of the scheme, another bus company expressed concern over how it would work across non-participating areas.