Таможенный досмотр уже завершён.

It is a set phrase meaning customs inspection or customs check.

• таможенный = customs / related to customs
• досмотр = inspection, especially an official or security-style inspection

So таможенный досмотр is not just any inspection; it specifically refers to one carried out by customs authorities.

Russian often uses an adjective where English uses a noun as a modifier.

So:

• English: customs inspection
• Russian: таможенный досмотр literally customs-related inspection

This is very common in Russian. Compare:

• железнодорожный вокзал = railway station
• паспортный контроль = passport control

So таможенный is simply the normal Russian way to say customs here.

Досмотр usually means an official, often fairly thorough inspection, especially by authorities such as customs, airport security, or police.

Some rough contrasts:

• досмотр = official inspection/search/check
• осмотр = examination/inspection/look-over, often more neutral
• проверка = check/verification, a broader word

In this sentence, досмотр is the most natural word because customs is carrying out a formal inspection.

Because завершён is the short form of the passive participle, and Russian commonly uses the short form in predicate position.

Compare:

• Таможенный досмотр завершён. = The customs inspection is completed.
• завершённый досмотр = a completed inspection

So:

• завершён = used as part of the statement about the subject
• завершённый = used before a noun as an attribute

This is a very common pattern in Russian:

• Работа закончена. = The work is finished.
• Законченная работа = finished work

In the present tense, Russian normally omits the verb to be.

So Russian says:

• Досмотр завершён.

where English says:

• The inspection is completed.

This is completely normal. Russian does not usually say a present-tense equivalent of is in sentences like this.

It agrees with досмотр, which is:

• masculine
• singular

The short-form passive participle changes for gender and number:

• masculine: завершён
• feminine: завершена
• neuter: завершено
• plural: завершены

Examples:

• Проверка завершена. = The check is completed.
• Работы завершены. = The works/tasks are completed.

Since досмотр is masculine singular, завершён is the correct form.

уже means already.

It shows that the action has been completed by now, often with a sense like it’s done now or it has already been finished.

So:

• Таможенный досмотр завершён. = The customs inspection is completed.
• Таможенный досмотр уже завершён. = The customs inspection has already been completed.

In context, уже can sometimes add a slight nuance of reassurance, impatience, or contrast, depending on tone.

Yes. Russian word order is fairly flexible, though the neutral version here is very natural:

• Таможенный досмотр уже завершён.

Other orders are possible, for example:

• Таможенный досмотр завершён уже.
• Уже завершён таможенный досмотр.
• Уже таможенный досмотр завершён. — possible, but less neutral

Changing the order can shift emphasis. The original sentence sounds straightforward and standard.

Yes, usually a little more formal or official.

Both can often mean finished/completed:

• Досмотр завершён.
• Досмотр закончен.

But завершён tends to sound more formal, bureaucratic, or official, which fits well with airport, customs, and administrative language.

That is why Таможенный досмотр уже завершён sounds very natural in an official announcement or formal statement.

The correct spelling is завершён, with ё.

In many Russian texts, ё is often replaced in writing by е, so you may also see:

• завершен

But the pronunciation is still zavershyón, and learners should know that the stressed sound is yo, not plain e.

Using ё makes the pronunciation clearer.

A helpful pronunciation guide is:

tamózhennyy dosmótr uzhé zavershyón

Approximate stress:

• таможенный
• досмотр
• уже
• завершён

A few pronunciation notes:

• ж sounds like the s in measure
• ш is a hard sh
• ё is pronounced yo
• досмотр has a consonant cluster, so pronounce it carefully: dos-MOTR

It is a full sentence.

Grammatically, the structure is:

• Таможенный досмотр = subject
• уже = adverb
• завершён = predicate

The only thing that is not said explicitly is the present-tense to be, because Russian normally leaves it out.

So even though English might feel that something is missing, in Russian nothing is missing at all.

Yes, that would also be grammatical and understandable.

However, there is a slight style difference:

• завершён = more formal, official, administrative
• закончен = more everyday, though still perfectly normal

In an airport or customs context, завершён sounds especially appropriate.