Steve Nicholson asked 24-year-old Caroline Harrison to marry him when her spirits began to fail after 10 hours surrounded by bodies in the sea.
The couple promised each other they would survive as they clung to each other for another 10 hours before they were rescued.
Mr Nicholson, 34, said: "I told her we should get married if we got to land and she said 'Yes'." He added: "I don't think we would have survived if we had not had each other. Caroline kept me going and I kept her going."
They were among only 47 people to be found alive after the cement-carrying ferry sank off Banda Aceh with 210 people on board on Friday night. Rescuers recovered 50 bodies by the time the search was called off last night.
The Britons, who are both from Eltham, south London, said the ferry had gone down in less than 30 seconds after it hit rocks. Mr Nicholson said he tried to get life jackets, "but everybody was fighting each other for them and the next thing I knew was that the boat was already sinking".
The wreckage of the ferry was also found last night, renewing hope that some people may still be alive inside. Meanwhile, in a live television link-up, Ms Harrison told her parents, John and Daphne Holbrook: "I don't know how we lived through it. It was a miracle."
Ms Harrison described how the couple survived for almost 20 hours in the water by clinging to a lifebelt.
"It saved our lives," she said. "We would never have survived without that. There were so many people dead it was just horrendous."
She described how she and Mr Nicholson kept their heads and stayed afloat. "I'm not even a very good swimmer," she said. "I hate the water."
At one point, the starving couple, their mouths parched from the sea water, saw some tomatoes and oranges floating towards them. "We didn't know if it was a miracle or a mirage. They tasted so good," she said.
"I just wanted to make it so we could be together."
Mr Holbrook said of Mr Nicholson:"I can't thank him enough for keeping her safe and bringing her back to us."Reuse content