Kierkegaard does describe eternity as related to the “fullness of time,” especially in The Concept of Anxiety and Philosophical Fragments. But he does not simply identify eternity with an infinite amount of time.

For Kierkegaard, the distinction is roughly:

• Time is characterized by succession: past → present → future.
• Eternity is not an endlessly extended temporal sequence. It is the “present” in a radically different sense—a fullness or simultaneity in which succession is overcome.
• The phrase “fullness of time” comes especially from Christianity: “when the fullness of time had come, God sent forth his Son” (Galatians 4:4).
• Kierkegaard interprets the Incarnation as the extraordinary point where eternity enters time. The eternal God becomes a temporal individual, Christ.

A particularly important formulation appears in Philosophical Fragments, where Kierkegaard contrasts the “moment” (Øieblikket) with ordinary temporal succession. The moment is the point at which time and eternity touch. It is therefore not merely a tiny piece of time; it is a qualitative intersection of the temporal and eternal.

So if by “fullness of time” you mean time brought to its completion or gathered into a fullness through its relation to eternity, then yes, that is quite Kierkegaardian.

But if you mean eternity = an infinitely long period of time, then no. Kierkegaard is quite opposed to that conception.

There is also a fascinating connection here with Augustine and Hegel: Kierkegaard's conception of eternity as fullness rather than endless duration is part of his broader attack on the idea that eternity can simply be understood as the continuation of temporal history.

If you want, I can also show you the exact passages in The Concept of Anxiety and Philosophical Fragments where Kierkegaard develops this idea, and explain how they relate to “the fullness of time.”

Yes. And looking at the actual passages makes the point somewhat more precise than my previous answer: Kierkegaard does not say simply that “eternity is the fullness of time.” Rather, the moment is the place where eternity enters time, and this moment is what he calls “the fullness of time.”

Here are the key passages.

1. The Concept of Anxiety, §IV: “The Moment”

In the Reidar Thomte translation, Kierkegaard first distinguishes ordinary temporal succession from eternity:

“The present, however, is not a concept of time, except precisely as something infinitely contentless, which again is the infinitely vanishing.”

Then comes the crucial formulation:

“The eternal, on the contrary, is the present. For thought, the eternal is the present in terms of an annulled succession.”

And immediately afterward Kierkegaard defines the moment:

“Thus understood, the moment is not properly an atom of time but an atom of eternity. It is the first reflection of eternity in time, its first attempt, as it were, at stopping time.”

This is extremely important for your question. Kierkegaard is not imagining eternity as more time—as an infinitely long succession of moments. In fact, he explicitly distinguishes eternity from succession.

The relationship is:

time = succession
eternity = annulled succession / the eternal present
the moment = eternity's reflection within time

So the “moment” is paradoxical: it is temporal, but it contains a relation to what is not temporal.

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2. The Concept of Anxiety: Christianity and the “fullness of time”

A few pages later, Kierkegaard makes the explicitly Christian connection. He writes:

“The concept around which everything turns in Christianity, the concept which makes all things new, is the fullness of time, is the instant as eternity, and yet this eternity is at once the future and the past.”

This is probably the passage you were remembering.

Notice the extraordinary formulation:

“the instant as eternity”

And then:

“this eternity is at once the future and the past.”

The point isn't that eternity is time in its entirety. Rather, in Christianity, a particular temporal instant can acquire eternal significance.

Kierkegaard's conception is therefore something like:

The fullness of time = the moment in which the eternal is present within temporal existence.

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3. Philosophical Fragments, Chapter II: “The Moment”

Here Climacus makes the point even more explicitly.

He asks what happens if the Christian claim is true—namely, that the eternal God actually enters history.

He writes:

“Now if things are to be otherwise, the Moment in time must have a decisive significance, so that I will never be able to forget it either in time or eternity; because the Eternal, which hitherto did not exist, came into existence in this moment.”

This is the really radical claim.

The Incarnation means that something happens in time that has eternal significance. Indeed, Climacus provocatively says that “the Eternal” comes into existence in the moment—meaning that the eternal God becomes historically present as the God-man.

And then comes the passage that answers your original question almost verbatim:

“And now the moment. A moment such as this is unique. To be sure, it is short and temporal, as the moment is; it is passing, as the moment is, past, as the moment is in the next moment, and yet it is decisive, and yet it is filled with the eternal. A moment such as this must have a special name. Let us call it: the fullness of time.”

That is the central passage.

What Kierkegaard means

The sequence is worth laying out carefully:

ordinary moment

→ short
→ temporal
→ passing
→ becomes past

but the Christian “Moment”

→ is still temporal
→ still passes
→ is filled with the eternal
→ therefore has decisive, eternal significance
→ is called “the fullness of time.”

So “fullness” does not mean that time has somehow accumulated enough duration to become eternity.

It means something closer to:

Time becomes “full” when eternity is present in it.

And this is why the Incarnation is so central. The Incarnation is not merely an eternal truth that happens to have a date in history. For Climacus, the eternal actually enters the historical, so that the historical moment becomes the locus of eternity.

A recent scholarly discussion makes exactly this distinction: Philosophical Fragments treats “the fullness of time” as more central than The Concept of Anxiety, with the Moment being simultaneously “short and temporal” and “filled with the eternal.”

One subtle point

This also corrects a possible misunderstanding of the phrase “eternity is the fullness of time.”

Kierkegaard's actual formulation is closer to:

The Moment is filled with the eternal, and such a moment is “the fullness of time.”

That's different.

In fact, The Concept of Anxiety gives us the philosophical structure, while Philosophical Fragments gives us its Christological realization:

Concept of Anxiety:
eternity ↔ time → the moment

Philosophical Fragments:
eternity ↔ time → the Incarnation → the Moment → the fullness of time

And this is why Kierkegaard's conception is so interesting: eternity doesn't abolish time. It gives a particular moment its ultimate fullness.

If you're interested, the next really fruitful step is to compare this with Augustine's conception of eternity in Confessions XI—because Kierkegaard's “eternal present” can initially sound Augustinian, but Kierkegaard makes the idea much more explicitly Christological and existential.