I would recommend adding a bridging router that would be connected to both networks. You can use pretty much any router with at least two Ethernet ports and that can run aftermarket firmware (like Tomato, OpenWRT, DD-WRT, and so on).
All you have to do in the router that connects the two networks it this:
Configure each of two Ethernet ports into different VLANs.
Assign each VLAN an IP address in one of your two networks.
Connect each port to the network that port's VLAN has an IP address in.
Make sure the router is configured to do routing. (This is the default in most distributions.)
Then, to make it work, you'll have to log into each of your two existing routers and add a route. For example, if the bridging router is
192.168.2.2, you'll need to add these two routes:
In the 192.168.1.x network, a route to 192.168.2.0/24 with a gateway of 192.168.1.2
In the 192.168.2.x network, a route to 192.168.1.0/24 with a gateway of 192.168.2.2
Note that computers in the two networks will be in different broadcast domains, so they won't easily discover each other. Depending on what tools you plan to use, there are various ways around this. For example, if you use Windows networking a lot, you can use a program (like nmbd) that synchronizes browse lists across the two networks.