Aaron Ramsey scored both goals as Wales secured their third appearance at a major tournament, four years after they reached the semi-finals of Euro 2016.
The Republic of Ireland, Scotland and Northern Ireland will all contest the play-offs in March, with Scotland ending their campaign with a 3-1 win over Kazakhstan and Northern Ireland losing 6-1 in Germany on Tuesday.
England are among the six top seeds for the draw on November 30, but defending champions Portugal and world champions France have missed out.
Gareth Southgate's side may have suffered their first qualifying defeat in 10 years at the hands of the Czech Republic, but they won their other seven games and finished with a goal difference of 31 to win Group A and a seeded place in the draw on November 30.
Belgium and Russia qualified comfortably from Group I, with Roberto Martinez's Belgium side sealing top spot with an impressive 4-1 win in St Petersburg and making it 10 wins out of 10 with a 6-1 thrashing of Cyprus.
Robert Moreno oversaw the latter stages of an unbeaten qualifying campaign which ended with a 5-0 win over Romania, but Luis Enrique was immediately re-appointed as manager five months after stepping down for personal reasons.
Italy rounded off their qualifying campaign in some style with a 9-1 thrashing of Armenia. Former Manchester City boss Roberto Mancini took charge of the national team following their failure to qualify for the 2018 World Cup and led them to 10 wins from 10 in qualifying.
Germany and the Netherlands both sealed qualification from Group C on Saturday with a 4-0 win over Belarus and 0-0 draw with Northern Ireland respectively. Germany ended up being seeded thanks to Holland dropping points and Joachim Low's side ended their campaign by beating Northern Ireland 6-1.
The surprise among the top seeds, Ukraine finished top of Group B ahead of Portugal and beat the reigning European champions in a key fixture in Kiev in October following a 0-0 draw in the opening group game in Lisbon.
Other qualifiers: Austria, Croatia, Czech Republic, Denmark, Finland, France, Netherlands, Poland, Portugal, Russia, Sweden, Switzerland, Turkey, Wales.
THE PLAY-OFF TEAMS
Scotland could only finish third in their qualifying group behind Russia and Belgium, but victory in their Nations League group gives Steve Clarke's side another chance to reach the Euro 2020 finals.
REPUBLIC OF IRELAND
Mick McCarthy's side narrowly missed out on automatic qualification after failing to beat Denmark in their final group game and a goal-shy side will likely need to find more firepower to advance from the play-offs.
A 6-1 defeat in Germany was hardly the ideal way to round off a qualifying campaign and manager Michael O'Neill has to combine his international duties with his new club job at Stoke before the play-offs.
Path A: Iceland, Bulgaria/Israel/Hungary/Romania*
Path B: Bosnia and Herzegovina, Slovakia, Republic of Ireland, Northern Ireland
Path C: Scotland, Norway, Serbia, Bulgaria/Israel/Hungary/Romania*
Path D: Georgia, North Macedonia, Kosovo, Belarus
*A draw will decide which of Bulgaria, Israel, Hungary or Romania would fill the empty slot in Path C, and which three would go into Path A.