もうすぐ着きます。

The phrase is a combination of common Japanese adverbs and a verb. もう (mō) has roots in Old Japanese and has evolved to express completion or imminence. すぐ (sugu) also has ancient origins, indicating proximity in time or space. 着く (tsuku) is a fundamental verb in Japanese, meaning 'to arrive' or 'to reach,' with its kanji (着) conveying the idea of 'to wear' or 'to put on,' extending metaphorically to 'arriving' at a place. The polite masu-form (〜ます) has been a standard part of Japanese honorifics for centuries, used to show respect to the listener. The combination of these elements creates a common and natural way to express imminent arrival in Japanese.