Buckley arrives next month from adtech company Loopme and Leonard will follow in October from Oath.
Spotify declined to comment on the appointments but it is understood they are part of an effort to better partner brands and agencies.
Buckley led Loopme’s agency sales team as vice-president of UK sales and strategic partnerships from the end of 2016 until this month. A Loopme spokeswoman credited his role in the company’s strong growth.
Leonard has been UK trading director at Oath and its predecessor AOL for two-and-a-half years, and has previously worked as account director at Microsoft and as group head at Global Radio.
Buckley’s earlier career included spells as digital commercial director at Telegraph Media Group and head of agency sales at Microsoft.
Patel has made the appointments nine months after joining Spotify from AutoTrader in November last year.
Spotify's UK revenues from subscriptions and advertising in the first six months of 2018 were up 30% year on year to €270m (£243m). The UK is the company’s largest market after the US and generates 11% of global revenues.