Netherlands player Cruyff died aged 68 in March.
He made his name as a forward with Ajax and Barcelona, and was named European footballer of the year three times.
The work on the Â£250,000 Catherine Street Court all-weather project is expected to take about two-and-a-half months.
Aberdeen City Council joined forces with the Denis Law Legacy Trust and the Cruyff Foundation for the development.
The Cruyff Court Denis Law will also honour the Aberdeen-born football great. Law starred for Manchester United and Scotland. He was named European footballer of the year in 1964.
There are almost 200 Cruyff Courts in more than 15 countries around the world.
Work to create a community sports facility named after football legend Johan Cruyff has got under way in Aberdeen.