The move leaves Ryanair as the only passenger airline operating from the Ayrshire base as Infratil, the New Zealand-based owner, attempts to sell what it has described as an "under-performing" airport.
Twice-weekly flights to Warsaw and Gdansk will switch to Glasgow in March, seven years after Wizz established services at Prestwick.
Stijn Vandermoere, the Hungarian airline's head of network development and scheduling, said market research had shown that its passengers mostly originated in Glasgow and north of the city and did not want to travel to Prestwick, which has seen passenger numbers tumble in recent years.
"We have talked to our customers and they have told us they want low fares, but they also want to be able to travel from an airport that is closer to where they live. A great deal of our customers are from Glasgow and north of Glasgow, so it makes sense moving there from Prestwick," he said.
Infrastructure firm Infratil put Prestwick up for sale last March, along with Manston airport in Kent, describing both airports as underperforming and saying it expected a deal to be completed by early 2013. Tom Wilson, group chief executive of Infratil Airports Europe, admitted the sale of Prestwick was taking longer than expected but said there were a number of parties interested in buying what he described as a "relatively complicated asset".
He said: "All the elements such as air maintenance, freight and training do take time to assess, along with uncertainty about aviation and the increases in Air Passenger Duty."
Passenger numbers have dropped by half since a peak of 2.4 million in 2006 as Ryanair relocated a number of its services to Edinburgh and axed flights to Stansted.
However, the airline announced last month it would start expanding services from Prestwick again this summer with new routes to Rzeszow and Warsaw Modlin.
Mr Wilson said Ryanair's decision to go head-to-head with Wizz on its Warsaw service last October was likely to have influenced the move to Glasgow.
"The issue about catchment may be correct but our information is that passengers value having a direct rail link to Prestwick, which they will no longer enjoy at Glasgow," he said.
A spokesman for the airport added the move would be "relatively insignificant" given that Wizz accounted for a small proportion of flights from Prestwick.
Amanda McMillan, managing director of Glasgow Airport, said the move would ensure Poland was served by the airport after a gap of 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.
"This announcement underlines our commitment to expanding our route network and delivering the routes and services our customers demand," she added.