The Swans will face Scottish side Hibernian or Malmo of Sweden as they return to European competition after a 22-year absence thanks to last season's Capital One Cup success.
If Swansea are to enter an all-British tie, Hibs will need to overturn a 2-0 deficit when they host Malmo in the second leg of their second qualifying round clash next Thursday.
Swansea will stage the first leg of the tie at their Liberty Stadium home on August 1, before making the trip to Scotland or Sweden the following week.
The Welsh club will also need to get through a play-off round if they are to make the group stage of the tournament.
While Hibs and Malmo, who were European Cup runners-up to Nottingham Forest in 1979, will provide potentially tricky opposition, Laudrup is delighted his side have avoided any long-haul journeys.
"I'm pleased with the draw," the Dane told www.swanseacity.net. "It was important for me that we avoided a long trip and the prospect of difficult weather conditions. Sweden or Scotland is perfect for us geographically.
"We also know the playing styles of both teams, so that is also a positive for us, although I would have preferred to be away in the first leg rather than home. But you can't have everything."
Malmo would appear to be Swansea's likely opponents, but Laudrup is not ruling out a Hibs comeback.
"Malmo is a huge club in Sweden with a proven record and proud history," he said.
"But I'm sure Hibernian will be in there fighting until the end."
Swansea last tasted continental competition courtesy of their Welsh Cup success back in 1991.
But their Cup Winners' Cup campaign was ended in emphatic fashion as they lost 10-1 on aggregate to a star-studded Monaco side managed by Arsene Wenger and including George Weah and Youri Djorkaeff.
On this occasion Swansea will enter Europe under the English flag, having qualified as representatives of the Football Association, as opposed to the Football Association of Wales.
Should Hibs manage to overcome Malmo it would mean the Edinburgh club's new signing Owain Tudur Jones would come up against his former side.
Wales cap Jones enjoyed a four-year spell with the Swans between 2005 and 2009.
"I'm sure Owain will be relishing that one," said Swansea club captain Garry Monk. "Whoever we drew would have been be difficult, but at least geographically it is one of the better ones. We are all looking forward to it."