The eruption of the Hunga Tonga-Hunga Ha'apai Volcano in January 2022 in the southwest Pacific islands of Tonga triggered a tsunami that was detected beyond the Pacific basin. Here we show its spatiotemporal signature as revealed by hundreds of publicly available coastal tide gauge records from around the world. The Tonga tsunami was characterized by a uniformly small leading wave that arrived earlier than theoretically expected for a tsunami wave freely propagating away from the volcano. In contrast, the largest waves, of up to +3 m high, were concentrated in the Pacific and their timing agrees well with tsunami propagation times from the volcano. While the leading waves were caused by a previously reported fast-moving atmospheric pressure pulse generated in the volcanic explosion, the large waves observed later in the Pacific were likely originated in the vicinity of the volcano although its generation mechanism(s) cannot be identified by the tide gauge data alone.