Ég hef búið í borginni lengi, en núna langar mig að flytja í sveitina.

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Breakdown of Ég hef búið í borginni lengi, en núna langar mig að flytja í sveitina.

• núna: now
• í: to
• mig: me

Questions & Answers about Ég hef búið í borginni lengi, en núna langar mig að flytja í sveitina.

Why is it Ég hef búið and not Ég bý at the start?

Ég hef búið í borginni lengi literally corresponds to English “I have lived / I’ve been living in the city for a long time.”

• hef búið = present perfect (have lived)
• bý = simple present (live)

In Icelandic, just like in English, when you mention how long something has been true up to now, you normally use the present perfect, not the simple present:

• Ég bý í borginni.
  = I live in the city. (simple fact about now)
• Ég hef búið í borginni lengi.
  = I have lived in the city for a long time. (emphasizes duration up to now)

So Ég bý í borginni is correct by itself, but when you add lengi (for a long time), the natural tense is Ég hef búið.

What exactly is búið here? Is it an adjective, a verb form, or something else?

búið is the past participle of the verb að búa (to live, to reside).

The important pieces:

• Infinitive: að búa – to live / reside
• 1st person singular present: ég bý – I live
• Past participle (neuter form): búið – used with the auxiliary hafa (to have) to form the perfect.

So:

• Ég hef búið = I have lived / I have been living

Unlike English, Icelandic participles agree in gender/number/case when used as adjectives, but with the auxiliary verb (hef, hefur, hafa, etc.) they simply make a perfect tense, like English have + past participle.