You'll need to configure a 'routing VIP' (or two), enabled only on the 'inside' VLAN(s) along with suitable SNATting.
"A BIG-IP is a deny by default device. It will not act as a router for traffic; static and attached interface routes are used only when handling traffic for a Virtual Server, NAT or SNAT. This behaviour can be changed by creating ‘routing’ Virtual Servers"
See the 'Emulating stateless IP routing with BIG-IP LTM forwarding virtual servers' section of this document for configuration information: http://support.f5.com/kb/en-us/solutions/public/7000/500/sol7595.html
Nimbostratus
