The "correct" solution is a [u]DIMMABLE constant current LED power supply[/u].*
The industry standard for these things is a 0-10VDC dimming signal or 10V PWM. So, you need a 10V source and a low-power transistor or MOSFET to "boost" the Arduino's PWM.
- Technically, they are controlled-variable current since the current depends on the dimming control signal.