Let's say life debts* are taken fairly seriously, particularly in difficult places like Tatooine and the poorer areas of Corellia. It's generally handled by favours; you could save that person's life in turn, or work for them for a few years, pay them off, or in some cases, marry them.

Han asks Luke to marry him at the end of ANH, stating he'd gladly take it as payment for the life debt. Luke, who's used to the concept of arranged marriages since poor families often liked to use marriage to move up in the world, accepts.

This marriage could either be the ceremony at the end of ANH, or after some time.

Bonus for:
1. Leia's reaction. She can understand and respect it. Or understand and not respect it. Or think they're both completely insane and doesn't understand why the hell life debts exist in the first place.
2. Han and Luke being affectionate to each other and pleased with their choice.
3. Han's proposition being both businesslike but also sort of : "You're hella cute and we're both hot I mean come on I risked my life for you I barely know you we're obviously meant to be."
4. Chewie's just pleased Han's found someone.
5. C3PO's worried since now he and R2 technically belong to Han as well.

*this happens more for strangers. I mean, obvs you're gonna save your nearest and dearest.