The airline will fly to the town on Mondays, Fridays and Sundays from May 1, all year round.
Flights will be from £36.99 one way, including taxes and charges.
The service is expected to be particularly popular with those visiting Ireland for The Gathering, a marketing campaign to promote the country.
Shannon, in County Clare, has long-standing cultural affinities with Glasgow and the business sector is also expected to welcome the link.
The Wednesday/Friday flights will depart from Glasgow Airport at 10.50am and arrive at Shannon at 12.15pm. The Sunday flight will leave at 2.55pm.
Simon Lilley, Flybe's director of marketing, said: "Flybe is committed to developing further its route network out of Glasgow.
"We have every confidence this additional new service will prove successful in offering an attractive and affordable way for travellers to access this growing business and leisure destination."
Amanda McMillan, managing director of Glasgow Airport, said: "The Irish market is very important for us and the addition of Shannon provides people in Glasgow and west Scotland with easy access to Limerick, which is the ideal base from which to explore the Irish west coast.
"Flybe has been very active in identifying new destinations it feels will work out of Glasgow Airport and with the convenient flight times we are confident this route will be a success."