Space tourist and adventurer Richard Garriott, the son of an astronaut, will officiate at the ceremony during the 90-minute flight.
The newlyweds are sure to have butterflies in their stomachs because the trip includes 15 rollercoaster-type dives, known as parabolic arcs, which last up to 30 seconds.
The jet plummets from 36,000 feet to 24,000 feet and then climbs back up--allowing passengers on the Boeing 727 to experience weightlessness.
"There's going to be that moment of expectation right before we are lifted up and I feel like I've waited my whole life for that," said Fulmore, a legal secretary.
"We will be one of the few humans who have experienced that."
The lovebirds had their wedding wardrobe especially designed for the occasion.
Finnegan will wear a multilayered white gown and Fulmore will be in a tux with tapered tails to ensure their clothes don't reveal too much.
The pair met at an NYU science fiction club in 2000 and began dating in 2002. They went to so many "conventional" weddings they decided to do something out of this world.
"Since this is the one time in our lives that we were going to do this [get married], we thought we should make it a once-in-a-lifetime event," Fulmore said.
"My mom thinks I'm absolutely nuts."
The honeymoon will be more low-key--a trip to Disney World--but you can bet they won't miss Space Mountain.
"I never wanted to have a normal wedding," said Finnegan, who works in animation production. "I couldn't picture myself walking down an aisle."
The flight costs, 200 per person and Finnegan and Fulmore are footing the entire bill themselves.
"I think we will spend some of our married life simply paying off the expense, but I think that weightlessness is probably the best metaphor for love that one can experience," Fulmore said.