Is it possible to use the same power source for the arduino and a high current I've need to control some leds which draw 300mA with an arduino (actually an atmega) and after some searching I think the following is the circuit I need, but I'm not really sure if the power source for the LEDs can be the same as for the arduino.
R1 = 1k
If the power supply has sufficient power and voltage stability, you can use it to power the LED and Arduino. However, the circuit is not entirely correct on the LED side, a current limiting resistor should be used in series with the LED. I would also recommend using a more powerful bipolar transistor or field effect transistor.