That shift is going pretty well. In the company's earnings report for the quarter ended June 30, Microsoft says it had a $12.1 billion "run rate" in its commercial cloud products.
In English, that means that if you take the amount of money Microsoft is collecting on cloud contracts right now, and extrapolate it out over a full year assuming no growth or churn, it would generate $12.1 billion for the year.
By way of comparison, Amazon said on its Q1 earnings call that its cloud services were on a $10 billion run rate. Amazon is expected to post Q2 earnings on July 28.
Here's what Microsoft's cloud run rate looked like prior to the June quarter:
Statista
Disclosure: Jeff Bezos is an investor in Business Insider through hispersonal investment company Bezos Expeditions.