The Glasgow-based carrier also said it will restart its Inverness-Dublin and Aberdeen-Bristol routes which were suspended during the Covid pandemic last year.
The Dundee route to Sumburgh comes as a major addition to the city’s small airport which currently only has flights to London City and Belfast City, both also operated by Loganair.
The UK’s biggest non-London airline will fly the route twice weekly from next May.
Up to four Inverness-Dublin flights a week will resume the same month.
Loganair’s Aberdeen-Bristol flights will restart five days a week from October 31.
In a further sign of its expansion into England, Loganair said it would launch another brand new route, between Teesside and Southampton, with up to six flights a week from March.
It said the link would enable passengers to and from Aberdeen to reach Southampton with one stop while being able to stay on the aircraft.
Loganair said Eastern Airways had announced plans to launch the route but later scrapped them.
Loganair has already announced its intention to resume international flights to Bergen and Stavanger in Norway next year.
Overall, Loganair said it planned to operate more than 1,300 flights a week on 76 routes in 2022.
The airline said official Eurocontrol flight data showed it was operating a greater proportion of its pre-pandemic routes than any other airline, and was one of only two European passenger airlines of any size running more flights than it did in 2019.
However, airline chiefs said its flights were dependent on passenger demand.
It has already cancelled its Aberdeen-Newcastle route this year because of poor demand.
The airline’s Donegal-Glasgow flights will end next month, and it scrapped the Edinburgh-Jersey route it planned to operate this summer.
Chief commercial officer Kay Ryan said: “We are looking to 2022 with optimism and continuing to connect more and more of the UK as we are able to do.
“Customer booking patterns will remain an incredibly important factor for us as we review which services we operate and which destinations we add either frequency or additional seat capacity to.”
Loganair had expanded its network by taking over many of the UK routes flown by failed rival Flybe, which collapsed in March last year.
However, many of these were suspended during the pandemic, some before Loganair had started operating them.
Inglis Lyon, managing director of Scottish Government-owned Highlands and Island Airports, which includes Inverness, Dundee and Sumburgh, said: “Loganair’s routes expansion and the increasing frequency of its services is a further indication the aviation industry is emerging from the pandemic and reacting positively to pent-up demand.
“I am particularly pleased our airports in Dundee and Shetland will offer direct flights which will provide greater connectivity between the two locations and also allow passengers to link to London City.
Loganair introduced a £1 per passenger “carbon offset charge” in July in the airline’s first step towards becoming carbon neutral by 2040.
It is believed to be the first overt compulsory environmental levy, which some airlines hide within their fares.