I would be careful with the circuit Anand posted... it's an unregulated charger and as you suspected, after the battery has fully charged, the output voltage goes up to around 17V. Do not leave the charger connected to your battery for long time or it will degrade it.
The circuit you posted looks like(a little hard to see) it's using a 3 terminal voltage regulator (LM117?) to generate a constant voltage. For a sealed lead acid it's around 2.25V/cell, so for a 12V battery, it works out to around 13.5V.
Initially, when the battery voltage is low, the voltage drop from V+ to the base of the transistor is high enough to turn on the transistor and turn on the voltage regulator IC. As voltage increase on the battery, it drops enough voltage to turn off the transistor and turn off charging.
I would say this is closer to what you want. You can invert the signal on the collector of the transistor to turn on/off the alarm. (low voltage - battery charging, alarm off, high voltage -battery charged - alarm on.)
Cheers.