Witnesses at the court tell TMZ ... the couple exchanged vows Saturday morning, and it was an extremely intimate affair -- the only guests were Christos' daughter, and a close friend.

Sources tell us both of their parents gave their blessings for the smaller courthouse wedding -- which they needed to be legally married in the U.S. before going all out, big fat Greek wedding style!

Yes, we're told Shaina and Christos will have a more traditional, and bigger, ceremony later this month in Greece ... with all of their family and friends.

'LIB' fans will recall Shaina had a strong connection in the pods with former costar, Kyle Abrams. Kyle and Shaina actually got engaged while on the reality series, before she called it quits and left the show. Kyle moved on with his other costar Deepti Vempati after filming ended.

Christos popped the question back in March, after nearly a year of dating. Clearly, Shaina's been down this road before, but this time, she's sealed the deal.