I need to do the same to avoid the usage of a proxy in OpenLayers.
Since I'm running Ubuntu 12.04, I've installed Tomcat 7.0.55, instead of the default 7.0.26 (installed from packages).
To add CORS headers, I simply added to $CATALINA_HOME/conf/web.xml
the following lines:
<filter>
<filter-name>CorsFilter</filter-name>
<filter-class>org.apache.catalina.filters.CorsFilter</filter-class>
<init-param>
<param-name>cors.allowed.origins</param-name>
<param-value>*</param-value>
</init-param>
</filter>
<filter-mapping>
<filter-name>CorsFilter</filter-name>
<url-pattern>/*</url-pattern>
</filter-mapping>
and then restart tomcat.
For example, when I try to fetch from Geoserver the URL http://development.localhost.lan/geoserver/wfs
from my application running on http://localhost:3000
I get the following headers:
Requested headers:
POST /geoserver/wfs HTTP/1.1
Host: development.localhost.lan
Origin: http://localhost:3000
X-Requested-With: XMLHttpRequest
(...)
Response headers:
Access-Control-Allow-Credentials:true
Access-Control-Allow-Origin:http://localhost:3000
Connection:Keep-Alive
Content-Disposition:inline; filename=geoserver-GetFeature.text
Content-Encoding:gzip
Content-Length:469
Content-Type:text/xml; subtype=gml/3.1.1
Date:Tue, 29 Jul 2014 21:31:08 GMT
Keep-Alive:timeout=5, max=100
Server:Apache-Coyote/1.1
This worked with Chrome (Ver. 35.0.1916.153) and Firefox (Ver. 31.0).