Simplest solution is to switch a basic NPN transistor on and off with your PWM output. Assuming it's a 5V microcontroller, that puts 5V on the base and about 4.4V on the emitter. A 440 ohm emitter resistor then gives you 10mA flowing through the transistor (collector to emitter, the base current will be trivial).
Connect however many LEDs you like in series to the collector, and they'll all have 10mA flowing through them. They'll drop whatever voltage is appropriate depending on their colour (about 2V for basic red, yellow, green, about 3V for blue and white), and the rest of the voltage is dropped across the transistor.
With a 24V main supply voltage, you should be able to run at least 5 or 6 LEDs this way. If you want a different current, just change the emitter resistor as appropriate. 4400mV/220ohm = 20mA etc.
Technically, the LEDs always run at the same brightness, and the PWM just switches them on and off. The more they're on, the brighter they'll look. So you're not actually changing/controlling the current at all. What you're doing is changing the average current over a period of time. The human eye does the rest.
Note that your schematic shows the LEDs in parallel, which is not what you want. A parallel configuration will divide the current between them. You want the same current through them, so they need to be in series. (Because current is conserved: What goes in one end, flows out the other and into the next. So you get the same current in every device - LEDs, transistor and resistor all have the same 10mA flowing through them.)
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