Geldof, 62, began dating 49-year-old Marine after meeting at a dinner party in Paris, reported Daily Mirror.
The couple hope the news will give their family something to focus on following the death of Geldof's daughter Peaches last month.
"Bob has proposed. She is over the moon. Jeanne Marine has been a rock and a tower of strength over this. I'm so excited for her I am bursting to tell someone.
"Bob and Jeanne have been through hell, but they are determined something positive will come out of it. After all the sadness, we need something to focus on which will bring joy and light," a source said.
"I've just got back from Texas and accompanied Jeanne to the funeral. It was, of course, terribly sad, but she told me that Bob had asked her to marry him out of the blue.
"I'm so happy for her. It makes you realise we all have to value what we have," the source added.