The FTSE 100-listed bookmaker said Hill would replace outgoing CFO Alex Gersh, who announced his intentions to step down in early March, in the autumn.
In its own statement, Saga said Hill would remain at the group until September, adding that the search process for a successor will start immediately with the over-50's holidays and insurance specialist to update the market as soon as this has concluded.
Hill was previously group finance director at housebuilder Bovis Homes.PLC (LON:BVS) and has held senior financial roles at travel company TUI AG (LON:TUI) and British gas-owner Centrica PLC (LON:CNA).
Commenting on the appointment, Paddy Power Betfair's chief executive Peter Jackson said: "We're delighted that Jonathan is joining us. He brings substantial strategic and operational finance experience in consumer businesses and I am confident he will make a significant contribution to Paddy Power Betfair's future success."
Hill added: "I am excited to be joining a business with great brands, differentiated products and substantial international scale. There are many opportunities to drive shareholder value and I look forward to being part of the team to deliver this."
Shares in Paddy Power Betfair were down 1.5% at 7,155p in mid-morning trading, while Saga shares lost 1.9% at 111.4p.