Other than promised of course…
Betroth is the word you seek.
“Engaged,” of course. But I think the word you’re looking for is “betrothed” – which means, in essence, that the person spoken of has undertaken vows to be married at a future date.
Affianced?
betrothed
Art
Isn’t betrothed more of engaged? I’m thinking of more along the lines of when parents arrange for their children to be married down the road. Like in Chinese or Indian cultures.
Would espoused since childhood work? Commited by their families to wed? I can’t think of any term in English that makes the distinction that you need.
When parents arrange their children’s marriage, it’s usually called an arranged marriage. 
maybe promised would be a good term for the situation you describe
How about promised? Or spoken for? I think both of those are vague enough to work for an arranged marriage.
affiance
transitive verb: to solemnly promise (oneself or another) in marriage
from the good folks at Merriam-Webster Online
Doomed. 
Bespoke, or bespoken is sometimes used in the context of arranges marriages.
Hey, Papermache Prince, here are two more words for you to look up…
verb ( as in engage, or betroth )
and
past participial adjective ( as in engaged, or betrothed, or promised… or, yes, doomed, screwed, caught, shackled, hooked, set to be wed, banned… ).
I thought of betrothed too… but would ‘pledged’ work? “X and Y are pledged to be married.” It doesn’t sound as formal as engaged, yet doesn’t have the sound of permanence as betrothed.
intended?
Pledged?
Perhaps “doomed” might be appropriate.