LED vs. CFL Bulbs on Modified Sine Wave Inverter
It will work better - you don't even need the inverter, run the LEDs directly from the DC, they will like it much better than AC, and you will save power.

If you do choose to use AC you will have to convert it back to DC before the LED can use it, which commercial LEDs do automatically as part of the package.

I would suggest you don't use commercial LED's with an Edison base bulb, instead get special purpose LED's that run directly on DC. They are cheaper and simpler.

Does the DC voltage vary? That might complicate things.