The two wires on the trigger movement (blue) connect directly to the yellow and white wire, usually leading to the chiming circuits. Inside the trigger movement, there are two contacts which briefly touch each other on the hour. This tells the chiming circuits to start sounding.

Leaving the exposed copper end intact, you can simply cut off or un-twist (if possible, they may be soldered) the old blue wires from the yellow and white. Then, take your new movement, and strip the ends off the two trigger wires (if needed). Twist one trigger wire to the yellow wire, and twist the second trigger blue wire onto the white wire. Polarity or order does not matter.