The airline, based at Robin Hood Doncaster-Sheffield Airport, currently operates scheduled flights between Cardiff and Anglesey.
It was among 11 successful bidders to the regional air connectivity fund for smaller airports, which also included a Flybe service between Dundee and Amsterdam, KLM’s world hub.
Minoan Air scrapped the Oxford route in 2013 after just five months, blaming a dispute with the city’s airport.
That came five years after Varsity Express started flights using a LinksAir-owned 18-seat aircraft on the route, but it went out of business after flying for only one week.
The UK Department for Transport said its start-up fund “allows air routes that are not currently commercially viable today to be introduced early, giving time for airlines to build passenger numbers and deliver a more sustainable service”.
It already supports Flybe’s Dundee-Stansted route, launched last year.
UK transport minister Robert Goodwill said: “Edinburgh and Dundee airports are vital engines for Scotland’s economy, connecting the UK and creating opportunities.
“That is why the UK Government backs new Scottish air routes, with our investment benefiting hard-working people across the country.”