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There is a purpose-designed Chinese chip exactly for your situation - control brightness of a LED strip based on PWM input. Compared to a bare MOSFET, this chip gives you higher efficiency, current-controlled (i.e. flicker-free) output and ability to drive LEDs directly (without current-limiting resistors).

PT4115, pretty cheap on ebay and other usual places.

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Well, the LED strip I use is a black box (from an electrical perspective). It just needs 12V, no external resistors.

So I just hooked it up to 12V via the MOS-FET. The PWM signal from the Arduino (plugged into the MOS-FET) does the job of changing the apparent brightness.

No need for magic chips in this context.

Your ledstrip probably also consumes about 15 watts per meter since integrated current limiting resistors dissipate most of the energy; a black box with the efficiency of a lightbulb.

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