Just in case it wasn't clear by now, Satya Nadella was absolutely the best pick to become Microsoft's (NASDAQ: MSFT) CEO. While Nadella has backed off slightly from his "mobile-first, cloud-first" mantra that he touted for his first couple years as CEO, incrementally de-emphasizing the mobile aspect of Microsoft's business while betting even bigger on the cloud and other areas like artificial intelligence (AI), Microsoft has been executing incredibly well under his leadership.

The software giant reported fiscal first-quarter earnings Thursday night, and Microsoft's commercial cloud business has hit a huge milestone.

Image source: Microsoft.

Commercial cloud growth is ahead of schedule

Microsoft's commercial cloud annualized revenue run rate has now hit $20.4 billion. In 2015, Nadella made a bold prediction that Microsoft could hit a $20 billion run rate by mid 2018 (the end of its fiscal year 2018). At the time, it was a rather tall order to fill, since the cloud business was then running at an annualized $6.3 billion. The company would have to triple the size of its business in just three years to hit that target. Microsoft just did it in two.

Data source: SEC filings. Chart by author. Fiscal quarters shown.

It's worth clarifying exactly how Microsoft calculates its annualized run rate. The company takes the last month of the quarter and multiplies those sales by 12 to get an annualized run rate.

In contrast, Amazon.com (NASDAQ: AMZN) calculates the annualized run rate for its Amazon Web Services cloud business by multiplying its most recent quarter's AWS revenue by four. The e-commerce titan also posted earnings last night, and AWS brought in $4.6 billion in sales, which represents an annualized run rate of $18.3 billion.

Image source: Getty Images.

AWS is the market leader for cloud infrastructure by a wide margin, but Microsoft's commercial cloud also includes other subscription-based offerings like Office 365 and Dynamics 365 that aren't directly related to cloud infrastructure. Microsoft does not directly disclose Azure revenue in absolute terms, which is its cloud infrastructure competitor to AWS and included in the company's broader commercial cloud. Azure revenue jumped 89% last quarter on a constant currency basis.

The cloud business is also incredibly profitable, which is helping Microsoft's overall gross margin. Here's CFO Amy Hood on the call Thursday night:

Our commercial cloud business had another quarter of robust revenue growth and material gross margin improvement. Revenue exceeded $5 billion this quarter, growing 56% year-over-year and gross margin increased 8 points to 57%, with improvement in each cloud service, most notably in Azure.