Victory over the Netherlands earned Britain a World Group play-off tie on 21-23 September.
BBC: Jamie Baker is among those challenging for a Davis Cup spot
Other World Group play-off winners were Belgium, Chile, Ecuador, France, India, Serbia and Sweden .
Koubek beat Greg Rusedski in the decisive rubber to relegate Britain from the Davis Cup World Group.
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If we can get a win, that would be fantastic and we can keep progressing into the world group.
Meanwhile, Federer helped Switzerland to a 3-2 win over Italy in Genoa to ensure World Group status for another year.
Federer will play in Switzerland's Davis Cup team when fight for World Group survival away to the Czech Republic in September.
And Roger Federer helped Switzerland beat Italy in the World Group play-off.
David Ferrer beat Stanislas Wawrinka 6-2 6-4 6-0 to give Spain an unassailable lead in the World Group tie after they had led 2-1 overnight.
BBC: David Ferrer secures Spain Davis Cup quarter-final spot
In World Group playoffs, Japan led Belgium 2-0 while the U.S. and Australia held the same advantage in their respective matches against Ukraine and Germany.
The defeat means Patrick McEnroe's U.S. team face a relegation playoff later this year to maintain their record of playing in the World Group every year.
CNN: Djokovic beats Isner in marathon as Serbia reach last eight
In another match delayed by weather, Australia won through to the World Group playoffs by beating Switzerland 3-1 on Monday, joining Germany, Spain and the United States.
The Czechs will next travel to Kazakhstan, who beat Austria 3-1 after returning to the World Group via a playoff following last year's first-round whitewash against Spain.
They will now play Croatia at home on July 9-11 in the quarterfinals of the premier team event in tennis after their first-ever victory in the World Group.
CNN: Djokovic beats Isner in marathon as Serbia reach last eight
Federer will get an early chance to put his U.S. Open disappointment behind him when he plays for Switzerland in a World Group playoff tie against Italy this weekend in Genoa.
Meanwhile, Petra Kvitova and Lucie Safarova gave Fed Cup champions the Czech Republic a 2-0 lead over Australia after the first day of their World Group tie in Ostrava on Saturday.
The Serbian women's team reached the World Group playoffs of the Fed Cup in 2007, but with Jankovic and Ivanovic in the ranks have the potential to challenge for top honors in years to come.
The Fed Cup World Group finals caps their year a week later, while for the men it's the Davis Cup final in the first week of December and a short rest before it all starts again.
The Fed Cup World Group finals caps their year a week later, while for the men it is the Davis Cup final in the first week of December and a short rest before it all starts again.
One break was also all that was required in the third set to seal a success that was Britain's first since September 2007 when they beat Croatia, in Tim Henman's final match, to book a place in the World Group.
With Djokovic leading the way and winning the conclusive rubber against John Isner, Serbia beat the might of the United States in the World Group first round earlier this month to reach the quarterfinals of the competition for the first time.
The opponents include the prominent Swiss-based (but Russia-linked) Trans World Group, which says that a ban on tolling is impractical, because Russian firms cannot be sure of always having the hard currency to pay for the continuous supply of imported ore they need.
Meanwhile, Serena Williams displayed her best form in roughly 18 months in winning at Charleston on green clay earlier this month, then led the U.S. Fed Cup team to a 5-0 sweep on red clay in Ukraine this past weekend, earning the team a berth in the World Group next year.
Djokovic, who helped Serbia reach the quarterfinals of the World Group of the Davis Cup for the first time in the week following his Dubai success, will next target the Masters events in the United States in early spring before turning his attentions to the French Open at Roland Garros as he bids to extend his grand slam tally.
The World Bank Group reports that more than 100 million primary school age children around the world remain out of school.
England's first World Cup group match is against USA in Lens on 8 September.
BBC: SPORT | Rugby Union | English | England 'must start playing well'
Algeria have been drawn in World Cup Group C along with England, Slovenia and the United States.
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The Rangers assistant manager was a television pundit as Algeria drew 0-0 with England in World Cup Group C.
BBC: Ally McCoist hails Madjid Bougherra's World Cup display
Mr. Zoellick is a former president of the World Bank Group, U.S. trade representative and deputy secretary of state.
Algeria meet Slovenia on 13 June in their opening World Cup Group C match, followed by games against England and the United States.
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