The easiest way to do this, as noted by Umar is, for example
mysql> SET GLOBAL time_zone = 'America/New_York';
Using the named timezone is important for timezone that has a daylights saving adjustment. However, for some linux builds you may get the following response:
#1298 - Unknown or incorrect time zone
If you're seeing this, you may need to run a tzinfo_to_sql translation... it's easy to do, but not obvious. From the linux command line type in:
mysql_tzinfo_to_sql /usr/share/zoneinfo/|mysql -u root mysql -p
Provide your root password (MySQL root, not Linux root) and it will load any definitions in your zoneinfo into mysql. You can then go back and run your
mysql> SET GLOBAL time_zone = timezone;