Register a Developer Application via the GitHub account that owns repos you wish to link.
See JIRA instructions for details. (This link also includes full instructions for this setup procedure.)
Log in to JIRA, go to Administration > Add-ons.
Click Source Control > DVCS accounts.
Click Link Bitbucket or GitHub account.
Behind the scenes, JIRA is registering a new app in the GitHub account's Personal Settings > Applications > Developer applications. This will generate a new OAuth Client ID and Client Secret.
Input OAuth Client ID and Client Secret. In the Team or User Account field, put the name of a GitHub account that has admin privileges for the appropriate repos.
Approve on GitHub OAuth via Authorize application confirmation.
Notes
DVCS account associated with specific user or organization.
JIRA DVCS connector automatically sets up Web Hooks on all repositories.