diff --git a/NEWS.md b/NEWS.md
index ff50e161fd4e5..1813cced9d100 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -124,6 +124,8 @@ New library features
   along with the type of the entries in a vector of new `DirEntry` objects to provide more efficient `isfile`
   etc. checks. `readdir(::DirEntry)` accepts a `DirEntry` as input and, like `readdir(::AbstractString)`,
   returns a `Vector{String}` of names. `DirEntry` is exported from `Base` ([#55358]).
+* Calls to `wait` on one-shot `Timer`s that have already triggered no longer throw `EOFError`. Previously
+  only the first `wait` returned and subsequent `wait` calls would throw ([#62539])
 * When the display height is too small to show any array entries, the `text/plain` array display
   (used e.g. by the REPL and when logging values with `@info` etc.) now shows as many entries as
   fit on a single line, truncated to the display width, instead of showing no data at all ([#62543]).
diff --git a/base/asyncevent.jl b/base/asyncevent.jl
index fe4b8c261231a..04ee3aa954bf6 100644
--- a/base/asyncevent.jl
+++ b/base/asyncevent.jl
@@ -74,8 +74,10 @@ Create a timer that wakes up tasks waiting for it (by calling [`wait`](@ref) on
 
 Waiting tasks are woken after an initial delay of at least `delay` seconds, and then repeating after
 at least `interval` seconds again elapse. If `interval` is equal to `0`, the timer is only triggered
-once. When the timer is closed (by [`close`](@ref)) waiting tasks are woken with an error. Use
-[`isopen`](@ref) to check whether a timer is still active. An inactive timer will not fire.
+once. When closing (by [`close`](@ref)) either a repeating timer or a one-shot timer before it has
+triggered, waiting tasks are woken with an error. After a one-shot timer triggers, all subsequent calls
+to [`wait`](@ref) return immediately, even if it is closed.
+Use [`isopen`](@ref) to check whether a timer is still active. An inactive timer will not fire.
 Use `t.timeout` and `t.interval` to read the setup conditions of a `Timer` `t`.
 
 ```julia-repl
@@ -105,6 +107,10 @@ false
 !!! compat "Julia 1.12"
     The `timeout` and `interval` readable properties were added in Julia 1.12.
 
+!!! compat "Julia 1.14"
+    Prior to Julia 1.14, only the first call to `wait` on a triggered one-shot timer returned,
+    and subsequent calls threw an `EOFError`.
+
 """
 mutable struct Timer
     @atomic handle::Ptr{Cvoid}
@@ -168,6 +174,9 @@ function _trywait(t::Union{Timer, AsyncCondition})
         t isa Timer || Core.Intrinsics.atomic_fence(:acquire_release, :system)
     else
         if !isopen(t)
+            # the :acquire read of isopen pairs with the :release store in uv_timercb, which
+            # sets `set` beforehand: a waiter observing the trigger-initiated close of a
+            # one-shot timer cannot miss the trigger on this recheck
             set = t.set
             if !set
                 close(t) # wait for the close to complete
@@ -195,7 +204,10 @@ function _trywait(t::Union{Timer, AsyncCondition})
         end
         iolock_end()
     end
-    @atomic :monotonic t.set = false # if there are multiple waiters, an unspecified number may short-circuit past here
+    if !(t isa Timer && iszero(t.interval_ms))
+        # if there are multiple waiters, an unspecified number may short-circuit past here
+        @atomic :monotonic t.set = false
+    end
     return set
 end
 
@@ -295,6 +307,8 @@ function uv_timercb(handle::Ptr{Cvoid})
     t = @handle_as handle Timer
     lock(t.cond)
     try
+        # this store must stay ordered before the :release store of isopen below, so that
+        # a waiter observing the close in _trywait is guaranteed to also observe `set`
         @atomic :monotonic t.set = true
         if ccall(:uv_timer_get_repeat, UInt64, (Ptr{Cvoid},), t) == 0
             # timer is stopped now
diff --git a/test/channels.jl b/test/channels.jl
index a04a0f8d70569..098ffb7b75fd7 100644
--- a/test/channels.jl
+++ b/test/channels.jl
@@ -595,6 +595,53 @@ let a = []
     @test timedwait(() -> a == [1], 10) === :ok
 end
 
+@testset "wait after closing a one-shot Timer (#34366)" begin
+    t = Timer(600)
+    close(t) # test assumes that thread won't get preempted for 10 minutes...
+    @test_throws EOFError wait(t)
+
+    t = Timer(0)
+    @test wait(t) === nothing
+    @test wait(t) === nothing
+    close(t)
+    @test wait(t) === nothing
+
+    waiters = [Threads.@spawn wait(t) for _ in 1:8]
+    @test all(w -> fetch(w) === nothing, waiters)
+
+    for i in 1:100
+        t = Timer(isodd(i) ? 0 : 0.001)
+        racers = [Threads.@spawn begin
+                for _ in 1:rand(0:8)
+                    yield()
+                end
+                try
+                    wait(t)
+                    wait(t)
+                    true
+                catch e
+                    e isa EOFError || rethrow()
+                    false
+                end
+            end for _ in 1:4]
+        for _ in 1:rand(0:8)
+            yield()
+        end
+        close(t)
+        outcomes = map(fetch, racers)
+        @test all(outcomes) || !any(outcomes)
+    end
+
+    t = Timer(0, interval=600)
+    @test wait(t) === nothing
+    waiter = @task wait(t)
+    yield(waiter)
+    @test timedwait(() -> !isempty(t.cond.waitq) && first(t.cond.waitq).task === waiter, 10) === :ok
+    close(t)
+    @test_throws TaskFailedException wait(waiter)
+    @test waiter.result isa EOFError
+end
+
 # make sure that we don't accidentally create a one-shot timer
 let
     t = Timer(Returns(nothing), 10, interval=0.00001)
diff --git a/test/threads_exec.jl b/test/threads_exec.jl
index f4676fdb2ada7..d9fbb33fc5e8b 100644
--- a/test/threads_exec.jl
+++ b/test/threads_exec.jl
@@ -629,7 +629,7 @@ for period in (0.06, Dates.Millisecond(60))
         close(async)
         @test_throws EOFError wait(async)
         @test !isopen(async)
-        @test_throws EOFError wait(t)
+        @test wait(t) === nothing
         @test_throws EOFError wait(async)
     end
 end