An easyjet flight from Split in Croatia was directed to Edinburgh, while a Jet 2 flight from Palma was diverted to Prestwick.
Both planes refuelled and are due to return to Glasgow Airport to try to land again.
Passengers writing on Twitter said they had been told that the flights had been disrupted because air traffic control at Glasgow had reported a mini tornado.
A spokesman for Glasgow Airport said: "Glasgow experienced a weather front which brought wind and weather patterns which caused easyjet EZY6812 from Split to divert to Edinburgh Airport.
"A Jet 2 aircraft LS190 from Palma was also diverted to Prestwick Airport. Both aircraft have refuelled and are returning to Glasgow airport. Glasgow Airport had remained open."
The Split flight was first due to land at 1.10pm, while the Palma flight was due to land an hour later.
A spokesman for Easyjet said: "Easyjet can confirm that flight EZY6812 from Split to Glasgow diverted to Edinburgh for additional fuel due to a longer than planned flight path as a result of thunderstorms in Italy and weather in Glasgow. The aircraft refuelled at Edinburgh and continued onto Glasgow Airport.
"The aircraft was an Airbus A319 with 143 passengers and six crew."
"The flight has landed into Glasgow now."
Heavy rain lashed the city for most of the morning as visitors and local enjoyed the last day of the Commonwealth Games.
Thousands of fans lined Glasgow city centre to watch the men's cycling road race.