Other Non-Current Assets - Schedule of Other Non-Current Assets (Details) - USD ($) $ in Millions	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2019
Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Abstract]
Deferred client conversion and start-up costs	$ 773.7	$ 433.8
ROU assets	262.0	292.6
Long-term investments	194.0	141.6
Deferred sales commissions costs	108.6	104.4
Contract assets	89.8	81.9	$ 47.5
Long-term broker fees	48.7	32.8
Deferred data center costs	24.3	24.5
Other	35.0	30.2
Total	$ 1,536.2	$ 1,141.9