It may be a while, acrobes, because there is no consensus. Some say a few months and others say several years. Dead roots will not generate additional juglone but they will release existing juglone as the roots decay. Because it's not that water soluble, the roots of the other plants have to get close or intermingle with the dead roots to be affected. Your best bet is to wait at least 1-2 years and take baby steps when planting tolerant varieties:

http://plantclinic.cornell.edu/FactSheets/WALNUTW.HTM
Note: Cornell says that the Pinxterbloom Azalea and the R. Exbury varieties Gibraltar and Balzac appear to tolerate juglone.

http://www.hort.wisc.edu/mastergardener/Features/misc/walnuttox/walnuttox.htm

http://www.pubs.ext.vt.edu/430/430-021/430-021.html

I had an established rhododendron bed that was invaded by roots from two black walnut trees in the wood that I had not paid attention to. When the rhododendrons started dying, I killed the black walnuts (girdled them) and also dug a trench about a foot deep cutting any roots that were coming into or out of the rhododendron bed. The bed came back. There was no further damage.

My advice would be to do the same. Dig a trench cutting any roots coming into or out of the bed since the roots will remain active years after the tree is cut down. My girdled trees were kept alive by the roots for 3 or 4 years.

Then when planting, dig sizable holes and put in all new soil. By the time the roots venture past the new soil, the problem should have subsided.

I'm also plagued by Black Walnut trees and have spent considerable time researching related issues (how I came across this post).

Good advice was given but, especially in reference to a case such as his, I've often wondered if there is any known material that can be added to the soil to neutralize or counteract the effects of juglone?

OFF to original question, but related to juglone.
I found (by pure accident) that hydrangeas of any kinds are not affected by juglone at all.
7-8 years ago I created a new bed around and between two mature Black Walnuts without thinking about possible consequences. Now two climbing hydrangeas reached 20-25' height and bloomed for the first time while 12 different macrophillas and serratas happily live and bloom there from the day one.

Some things that grow under black walnut are:

Tolerant grasses

Tall fescue and Kentucky bluegrass grow well near black walnut except during drought conditions when soil moisture is low. When moisture is adequate these grasses may grow better under walnut trees than in other parts of the lawn, possibly because the soil may be more basic. Soil under black walnuts tends to be alkaline, with the pH often 0 .7 points higher than beyond the roots, thus influencing the growth of many different plants.

Tolerant trees and shrubs

* arborvitae, American
* ash, white
* barberry
* beech, American
* birch, black; 'Heritage' river
* boxelder
* buckeye, Ohio
* catalpa
* cherry, black
* crabapple
* daphne
* dogwood, flowering
* elderberry
* elm, American
* forsythia
* fringetree
* goldenraintree
* globeflower
* gum, black
* hawthorn
* hemlock, Canadian
* hibiscus
* hickory
* holly, American
* honeylocust
* honeysuckle, amur; tatarian
* hydrangea
* lilac
* locust, black
* maple, red; sugar; black; Japanese
* ninebark
* oak, white; red; scarlet
* pawpaw
* pear, callery
* pine, Virginia
* privet
* red cedar, eastern
* redbud, eastern
* sassafrass
* serviceberry
* silverbell, Carolina
* spruce, Norway
* sumac
* sweetgum
* sycamore
* tulip tree
* viburnums (some species)
* witchhazel

Tolerant vines, ground covers and flowers

* anemone
* aster
* astilbe
* bee balm
* begonia
* bittersweet
* calendula
* clematis (virginsbower)
* coral bells
* creeper, Virginia
* daffodil
* daisy, shasta
* daylily
* evening primrose
* fern
* geraniums, hardy
* goldenrod
* grape, wild
* hollyhock
* hosta
* hyacinth, grape; oriental
* iris, siberian
* ironweed
* jack-in-the-pulpit
* lamb's ear
* liriope
* lobelia
* may apple
* morning glory
* mullein
* phlox
* primrose
* raspberry, black
* rose, wild
* rudbeckia
* scilla
* sedum
* speedwell
* spiderwort
* St. John's wort
* sunflower
* trillium
* tulip
* violet
* wisteria
* yarrow