Lars Lagerback's side drew with Kazakhstan to book its place at a first major international tournament while the Czechs saw off Latvia to seal their progression.
Czech Republic and Iceland have booked their places at Euro 2016 after securing the top two positions in Group A.
Both teams sit on 19 points after eight matches and cannot be caught by third-placed Turkey, which will now battle it out with Netherlands for a playoff spot.
Czech Republic took advantage of Netherlands' 3-0 defeat to Turkey as goals from David Limbersky and Vladimir Darida helped it to victory over Latvia.