"I've been thinking about asking her to marry me for a long time," said Paul in an "Elimination Station" video released on cbs.com on Monday. "If I do it now, it might lift her spirit. I think Jessica will say yes. I hope so."
Paul, a 28-year-old day trader from Aptos, CA, and Stout, a 27-year-old freelance editor from Larkspir, CA, got engaged after their The Amazing Race ouster while at Elimination Station in Vietnam.
"He proposed and I said yes," said Stout in the video. "So many emotions. Totally unexpected and crazy! I had no idea. I'm happy."
Paul said while he had hoped to propose to Stout -- whom he had been dating on-and-off for seven years -- on the finish line mat, they didn't quite make it that far. Still, he's glad that he was able to brighten Stout's mood.
"Jessica's mood is greatly improved since I proposed to her," he said in the video. "The race definitely solidified that she's going to be a great wife and stand by my side regardless of the situation."
Stout added that she also thinks their relationship will "last."
"We've been through every type of hardship possible and we're still here. We're a team no matter what," she said.