Hi.. i encountered same issue early this month..offer letter signed however my current boss counter offered and same time accomodate my relocation request.
so i just inform the HR / hiring personnel honestly followed by an apology for the inconveniences caused..i reckon u need to do it quick n not delay any longer..
imo ur new emplyer will not want you with them if they have the slightest idea tt you have the intention of leaving the co even before commencement..better to have a no-show than turning up and throwing in ur resignation letter like what, say the 3rd day of you being there..?

plus they wont take the time /spend money to sue you..they need to find someone to fill in ur position pronto
guess HR will probably record down somewhere.. however even if they do, they'll probably discard it after a few years..its not like u r involved in fraud or stole co's $..no big deal, so dun worry here