But the Aberdeen-born No. 9 is looking forward to joining up with the Warriors, who shocked European rugby with victory against giants Toulouse in France two weeks ago.
"Playing in France has been a fantastic experience and I've learnt a lot," said Cusiter.
"I now look forward to a successful end to the season with Perpignan before returning to Scotland in the summer.
"Both Scottish pro-teams have been getting good results recently and Glasgow have made their future intentions clear with some great performances, especially with the recent win over Toulouse."