The Help Centre has:
You can also accept your own answer, but you must wait 48 hours to do so. After all, someone else may come along with an even better solution to your problem!
That link leads to the blog entry Jeff Atwood wrote on the subject.
Now, there are some special rules around owner-accepted answers, to
Wait 48 hours. You must wait 2 days from the time you originally asked your question before you can accept your own answer.
This gives other users a chance to answer the question in good faith,
and earn the accepted answer.
No change in sort order. Normally, accepted answers are “docked” under the question. This is not true for owner accepted
answers; they stay in standard sort order like any other answer.
No reputation is earned. Normally, accepted answers confer +15 rep to the answerer and +2 to the owner. Owner accepted answers do not
earn rep (or badges) for anyone.
I was initially very much against this, but several commenters in the
Why Can’t I Accept My Own Answer? post convinced me that, with a few
rule tweaks, it could work.
There are additional links you can follow there too.
Finally, main meta FAQ has How does accepting an answer work?
Can I accept my own self-answer?
Yes; if you've self-answered your own question, you can mark your answer as the accepted answer. There are some differences, though, that exist in order to ensure everyone
gets a fair shot at answering:
- Accepting your own answer won't award you any reputation.
- The question must be at least 48 hours old before you can accept a self-answer.
- Self-answers that are accepted won't be pinned to the top.