From another google search on switching time -
To address the question, first a distinction needs to be made between phosphor LEDs (#1) (e.g. white LEDs, possibly some green LEDs) and direct emission LEDs (e.g. most visible color LEDs, IR and UV LEDs).
Direct emission LEDs typically have a turn-on time in single-digit nanoseconds, longer for bigger LEDs. Turn-off times for these are in the tens of nanoseconds, a bit slower than turn-on. IR LEDs typically show the fastest transition times, for reasons given ahead.
Special purpose LEDs are available, whose junction and bond-wire geometries are designed specifically to permit 800 picosecond to 2 nanosecond pulses. For even shorter pulses, special purpose laser diodes, in many ways operationally similar to LEDs, work all the way down to 50 picosecond pulses.
As pointed out by @ConnorWolf in comments, there also exist a family of LED products with specialized optical beam shaping, that boast pulse widths of 500 to 1000 picoseconds.
Phosphor type LEDs have turn-on and turn-off times in the tens to hundreds of nanoseconds, appreciably slower than direct emission LEDs.