08/03/2013 at 08:10 PM EDT
Elle Macpherson married billionaire Jeffrey Soffer in what was described as an "intimate" wedding in Fiji, PEOPLE has confirmed.
"Jeff and Elle eloped a month ago," the source tells PEOPLE, explaining that the groom is very low-key and likes to do things in private. "They wanted to keep it a secret."
The couple's original plan was to marry this fall in Aspen.
"They are very happy and head over heels in love," the source also tells PEOPLE.
The "day wedding" ceremony took place "mid-July" before "about 15 guests" – friends and family – inside a villa at the luxury Laucala Resort in Fiji, a hotel rep told PEOPLE's Australian sister publication, WHO
The Australian supermodel's two sons, Flynn, 15, and Cy, 10, participated in the ceremony, and while the immediate wedding party holidayed at the resort for a week, their guests arrived at various times before the wedding.
Another source tells PEOPLE that Don Soffer, Jeff’s dad, was also at the ceremony.
"This is such a joyful time for Elle and Jeff," a source tells WHO. "They are both thrilled." A family friend adds: "Jeff's really normal and a relaxed kind of person. In that way, actually, he's almost Australian. [The family] think he's great."
Macpherson, 49, who was previously married to photographer Gilles Bensimon, became engaged
to the Miami-based real estate developer in March this year.
The pair dated for two years before splitting in March 2012 and then rekindled their romance after Soffer was injured in a 2012 helicopter crash in the Bahamas.
Macpherson's two sons
are from her relationship with ex-boyfriend Arpad Busson, and she is currently hosting Britain & Ireland's Next Top Model
Reporting by MIA McNIECE and WHO STAFF