Why won't my security lights turn off after I upgraded to LED bulbs?
This is common with older security sensors. (The sensor needs a small amount of power to function.  To avoid wiring a neutral wire, they are wired in series with the bulbs, and power themselves by leaking a small amount of current through the bulbs - halogen bulbs don't mind this.)  

The simplest solution is to replace just one of the bulbs with incandescent or halogen.  it can be of a lower wattage. The rest of the lights can remain LED. 

The harder option is to replace the sensor/switch with a modern type, however this will require a neutral wire at the switch. (In this situation, the sensor gets its own power from hot+neutral, and does not need to leak any power through the bulbs.) This will save between $2 and $7 per year by using less power.