The pair married in Zapellar, Chile, and the cereony was carried out in both English and Spanish, with the pair reading out loud stories about how they met before exchanging vows.
The brunette beauty wore a stunning Vera Wang gown - although she almost had to find a last-minute dress when the frock was held at customs for over a week.
Lorenza also wore a crown of orange roses in her hair, while Eli wore an Isaia tuxedo.
The stunning model posted a candid shot on her Instagram page after the wedding, showing off her dress and crown of flowers, while sporting a pair of white sunglasses and a glass of champagne.
US Weekly revealed that the newlyweds and guests headed to the Cachagua Polo Club after the ceremony for food, drinks, dancing and fireworks.
"There was a singer from Iceland, Brazilian dancers and a standee for My Big Fat Chilean Wedding that everyone posed with!" a source told the publication.
"At midnight roast lamb was served and people drank and danced until 4am."
Guests reportedly snacked on popcorn which was served in boxes featuring images from the pair's movies including Aftershock and Green Inferno.