The `Paparazzi` hitmaker and Luc Carl reportedly professed their love for one another in an intimate moonlight service on the Greek island of Crete last week.
A source said: "It was their first step towards marriage. They both dressed up and said beautiful handwritten vows.
"They then exchanged rings in a spiritual service and drank shots before sitting down to a lovely private dinner at a tiny restaurant.
"They wanted to show that they are committed to each other and want to spend the rest of their lives together. They are still planning to marry, but that will come later when she has the time to plan a big Italian-style wedding."
Gaga wore a long white dress which fastened at the stomach for the ceremony, which was witnessed by a handful of close friends, while Luc donned a white suit jacket and silver zebra print leggings.
The eccentric singer is said to have realised the strength of her feelings for Luc following the recent death of her grandfather Joseph Germanotta.
The source added to Grazia magazine: "Since her beloved grandfather died last month, Luc has been her rock and she`s also had a reminder of just how short life is. She says he`s `The One` and she doesn`t want to lose him ever again."