Google started it with their Tensor chip in 2016 (now in its third generation) followed by the Edge TPU in 2018. Last year Amazon announced their own Graviton chip which is based on the ARM architecture (now in its second generation). In fact, the only cloud companies of the top five (Microsoft, Amazon, Google, IBM, Oracle) that are NOT making their own chips are IBM and Oracle. IBM sold their semiconductor division to Globalfoundries in 2015 and Oracle recently abandoned the SUN Microsystems IC team they acquired in 2010 for $5.6B, ouch.
Source: Intel vs AMD vs Google vs Amazon vs NUVIA – Semiwiki