Yuichiro ABE

Plug-in to synchronize the two WordPress
And synchronization of theme folder 
And synchronization of the plug-ins folder 
And synchronization of media 
And conversion (the serialized data including) the host name in the database
Plug-in to be used, for example, when you publish WordPress from a development environment to a production environment

WP Publisher

"Plug-in to Upload WordPress site Dev to Publish by one click".

PiotrPress

Clearcode

This plugin allows you to automatically send changes to your GIT repository, immediately after any update is made on your site.
If you store the source code of your website in the GIT repository, you can use this plugin to automatically send changes in the website’s code to the repository after each update. 
The plugin checks for updates (core, plugin, theme, translation) in a selected time interval, creates a new commit, and makes a push to the GIT repository. 
The plugin supports automatic WordPress updates. After each action the plugin saves the status to logs which are available through wp-admin and also are sent by email to defined recipients.

CC-Update

This plugin allows you to automatically send changes to your GIT repository, immediately after any update is made on your site.

WP Publisher vs CC-Update