Scudamore was at the helm of the organisation for nearly 20 years, overseeing its growth into the world's most lucrative soccer league and global money machine.
The 59-year-old will join a committee of sports and business executives led by Damon Buffini, former head of private equity group Permira, tasked with increasing income from the biennial team golf competition between Europe and the United States.
The committee includes Europe's victorious 2014 Ryder Cup Captain Paul McGinley, Premiership Rugby chairman Ian Ritchie, European Tour chief executive Keith Pelley and its deputy CEO Guy Kinnings.
"The success of The 2018 Ryder Cup in France demonstrated the global appeal of the modern-day Ryder Cup, but there remains significant growth potential," European Tour chairman David Williams said in a statement.
A record 270,000 fans witnessed Europe beat United States for the Ryder Cup crown at Le Golf National on the outskirts of Paris last September. The victory was Europe's seventh in the last nine contests.
A report compiled by researchers from Sheffield Hallam University's Sport Industry Research Centre found that the tournament boosted economic activity in France by around 235.7 million euros (£209.5 million).
The three day match broadcast reached over 40 global TV networks to a total household reach of around 620 million.
"This committee will look at ways of optimising that while also protecting the contest's rich heritage," Williams said, adding it would explore opportunities to grow revenues and profits from the 2022 edition in Italy and beyond.
"I am delighted to welcome Ian and Richard to the committee. They will bring valuable insight from their time in the business of other sports, to add to the considerable golfing expertise brought by Paul, Keith and Guy."
The Ryder Cup is jointly administered by the European Tour and the PGA of America, with the 43rd edition of the competition set to be held in Whistling Straits, Wisconsin in 2020.
(Reporting by Hardik Vyas and Shrivathsa Sridhar in Bengaluru; Editing by Simon Jennings and Christian Radnedge)
