Replace Apache server with F5 as reverse proxy

This F5 article tells you exactly how to do it, complete with diagrams and sample configuration. Basically you need two features working together: an LTM Traffic Policy and an LTM Rewrite Profile.

However, you must beware of the fact that as of this time, the Rewrite Profile referenced in the document is apparently case sensitive. Mod_Proxy rules like ProxyPass and ProxyPassReverse are not. And to my knowledge, there is no way to make the LTM Rewrite Profile case insensitive (I have asked the question on DevCentral about case sensitivity and am trying to figure out if there is some way I'm not aware of to change it).

If you are confident all your URLs will come in in lowercase, you could still use it. However, if you are not, then I would recommend using the Traffic Policy as shown in the document for pool routing, but consider other means to rewrite the request and response URI references, such as more traffic policy rules or an iRule.