What is the best way to turn down a job after you have signed the offer letter?

I would first talk to the hiring manager over the phone explaining honestly your position followed up by a letter with the same information to formalize it. Turning down a job after you had signed an offer letter is unfortunate and will not look good no matter how you spin it so it is something you should only do once in your (hopefully early) career, so if you need to pull this particular trigger, make sure this is reeeeealy it!!  I have had in the past one or two people back out of signed offer letters and why I understand and would not want the person to be unhappy, if I encounter that person’s resume at another place or time, I would not be able to consider the person again - the impression I was left with the first time is the person is not capable of making a good decision and/or can’t stand behind a promise, both being paramount in the professional capacity and life in general.

I would draft an email, apologizing for accepting the offer and now backing your acceptance off. Tell them that another job which you feel is a better fit for your skills and interests and you have accepted that offer. Tell them that you are flattered to have been offered a job in their organization and hope to cross paths with them some day in the future. And then I would call the recruiter for the first job and explain this over the phone, while simultaneously sending the email. Be as nice and as professional as you can be. Good luck. 

There's no good way, but the best way of making a bad situation is to immediately tell the hiring manager that you are backing out.  They might get quite upset, but the longer you wait, the more upset they will be.

I am unfamiliar with signing offer letters. Is it a contract between you and the company? If so, you shouldn't back out unless you are under hardship and it should also offer you some protection against the company cutting you before you start. Is it simply something that commits you to the company informally? As I remember, you would sign documents becoming an official employee in HR on your first day. Before that, you are at best a maybe employee.The best thing to do is sign nothing committing you to a position until they make a commitment to you on the first day. The company can call you the day you move and dump you.Is this something recruiters came up with?

As another contributor says, there is no "good way".   Remember it is an Offer Letter. That means that they are offering you the job/work, you have the right to turn down the offer.  The definition of a contract is offer and acceptance to enter the contract; whichever form that may be.  You can withdraw your offer as much as they can withdraw theirs before the start date, although strictly speaking you should give the reasons why you do not want to proceed, but you are certainly not obliged to. Word it in away that you do not "burn your bridges, you may not get a second chance. Just be careful you do not make this a habit though, because word can soon get around that you may not be seen as reliable.

Jessica Stielau is spot on. I couldn't have said it better! The only thing I could add is if you know of someone who would be good in the position you're turning down and is looking for a new job, give them your friend's name and contact information.

So be 110% sure this is what you want to do and just do it, but make sure you give them enough Termination notice stipulated in your contract, otherwise it will fall back on you as bad play. As if making an illegal / cheating move in a board game like Chess.

I go along with Jessica... but I would think carefully before doing this. Reputations are important in business.  You didn't have to make the agreement. No one had a gun to your head.  but you did. Backing out now is a low class move and there is no way around that.  DONT do this again.  Twice in a career will probably be enough to kill it.