Scotland must beat Holland over two legs if they are to reach the European Championship finals in Portugal next summer.
Berti Vogts side qualified for the play-offs following Saturday's 1-0 home win over Lithuania.
The game will see Holland coach Dick Advocaat return to Glasgow after leaving Rangers last year.
Scotland have not beaten the Dutch since 1982. The sides last met in a 0-0 draw in Arnhem three years ago.
Russia, runners up to Switzerland in Group 10, stand in the way of Wales as Mark Hughes' side look to the finals.
Wales secured their play-off place some time ago but blew the chance to qualify automatically by losing three of their last four qualifiers.
They have never played Russia but did draw 0-0 with the Soviet Union in Swansea in 1987.
Wales manager Mark Hughes said: "We have got to be reasonably happy with the draw. We are playing the second leg at home and I think everyone's view is that is an advantage.
"Russia have had some great players in the past so we know it will be a test and now we just have to do all the research, look at all the videos, to make sure we know about their players of the present."
"As long as we avoided Holland and Spain, that was the main thing, so we've got to be quite pleased with the draw."
Wales have only ever qualified for one major tournament in the past, the 1958 World Cup.
Euro 2004 play-off draw:
Latvia v Turkey
Scotland v Holland
Croatia v Slovenia
Russia v Wales
Spain v Norway
(Ties to be played on November 15th-16th and 18th-19th)
Under-21 draw:
Germany v Turkey
Portugal v France
Denmark v Italy
Serbia & Montenegro v Norway
Belarus v Poland
Sweden v Spain
Switzerland v Czech Republic
Croatia v Scotland