I went through this recently,

I had 3 offer letters pending or in hand with still yet 2 other interviews taking place . My goal was initially set on the highest salary bid while I took some time to decide on the offers . While I was thankful that several companies had chosen me as their top candidates and still yet other companies had high hopes , A long-shot company made a surprise relocation offer to add to their offer letter. This left me in a very odd position in that I was expected to start a local position
that I had interviewed with over a month passing several tense rigorous technical tribunal styled interviews which few ever passed let alone aced and then comes along a tech company in a mad dash to get talent in without ever even doing a face to face over nighting a really generous relo check .The kicker for me was the title, company industry
and the city I would be relocating to which made me choose the long shot offer.
But how to break the news to the other companies without burning bridges or offending head hunters that seemingly went out of their way for you ? Seems like there never really is a good way other than to be honest when you're the client's top pick .