Well you could use chemicals such as glyphosate, but given you want to grow edibles there, the healthiest and safest option is actually to dig them out, whilst at the same time digging the area over and incorporating organic material such as well rotted composts. Unless you want to grow root crops like carrots, that is, they do not appreciate animal manure composts, but are fine with other kinds. Glyphosate can remain present in certain soils in certain conditions, and may be uptaken by any crops you grow there for anything up to a couple of years, despite claims that it leaves no trace after use. Many other chemical herbicides make the same claims, and whilst I might not mind risking it for ornamental plants, I wouldn't be too keen for an area where I intend to grow food.
UPDATE: I came back to add something and you'd accepted the answer already, but I wanted to say, if you don't intend to plant the area for a year, you could just cover it with thick, black plastic, anchored down firmly, to exclude all light, air, and moisture, but it would need to be in place for at least one year.