The announcement by Wizz Air means the only firm to operate passenger flights out of Prestwick will be Ryanair, as of March 1.
Wizz has operated twice-weekly flights to the Polish cities of Warsaw and Gdansk since 2006.
Its relocation to Glasgow will be more convenient for its customers and will attract new passengers, the firm said.
Airline crew will move with the flights, Wizz said.
"Wizz Air is pleased to announce these two new routes operating from Glasgow Airport, giving more consumers access to Wizz Air's low fares and great customer service," head of network development Stijn Vandermoere said.
"Our popular low fares have strongly grown our business in four UK airports and we're already the number two airline at one of London's main airports. We believe there is also significant growth potential in Scotland and our move to Glasgow Airport is a step towards future passenger and route growth.
"We are confident that Polish visitors to Scotland will embrace the convenient airport location and we urge Scottish consumers to try Wizz Air's award-winning service and low fares."
Prestwick Airport has been up for sale since March last year.
In December Ryanair announced an expansion of flights at the Ayrshire base and the airline's chief executive Michael O'Leary said the firm has an "unbreakable commitment" to Prestwick.
A spokesman for Prestwick Airport said: "The loss of Wizz from March is disappointing after a long, positive and productive relationship but is relatively insignificant as its flights-only account for a very small percentage of our total summer schedule.
"Our long-term partner Ryanair, on the other hand, has once again demonstrated its commitment to Prestwick by increasing capacity here by 10% to 27 routes for summer 2013, launching two new services to Rzeszow and Warsaw, thereby boosting our passengers to 1.4 million per annum and providing 95 low-cost flights a week to popular destinations such as Tenerife, Alicante, Faro and Corfu.
"This gives Scots an even greater choice of value-for-money summer destinations and is a further boost for the local economy, with more visitors to Scotland coming through the airport gateway. So we're looking forward to a superb summer here at Prestwick."
Mr Vandermoere said the future of Prestwick had no bearing on the decision to move Wizz to Glasgow.
"We are a private business and need to do what is right for the customers and we're trying to make sure we can offer the lowest fares at an airport close to consumers.
"We don't concern ourselves with the airports themselves. What we ask of them is that they offer us the lowest charges as possible so that we can pass that on in low fares."
The Wizz flights to Warsaw and Gdansk will be the first connecting Glasgow Airport to Poland in around 15 years.
Managing director Amanda McMillan said: "We are thrilled to welcome Wizz Air on board which is yet more good news for Glasgow Airport. Not only will it provide our customers with greater choice, it will further strengthen our connectivity with some of Europe's major cities and it means we can add Poland to our long list of destinations after an absence of more than 15 years.
"Wizz Air is an ambitious and rapidly growing airline which carried over 12 million passengers in 2012 alone, and we are looking forward to working alongside the team at Wizz to ensure it enjoys further growth and success at Glasgow."