Cousins was killed alongside his fiancée, OK! Magazine arts editor, Emma Bowden, her 11-year-old daughter Heather, and his sons, Edward, 23, and William, 25.
Gareth Morgan, the Australian pilot of the seaplane – which belonged to a company running sightseeing tours – also died in the crash.
In a statement on Tuesday, Compass chairman Paul Walsh paid tribute to Cousins, 58, and his family, from Tooting in south-west London.
"We are deeply shocked and saddened by this terrible news,” Walsh said.
“The thoughts of everyone at Compass are with Richard's family and friends, and we extend our deepest sympathies to them.”
The family were reportedly flying back to Sydney from an exclusive waterfront restaurant in Jerusalem Bay on New Year's Eve when the plane plunged into Hawkesbury River, about 30 miles north of the city.
Investigators said it could be many months before the cause of the crash is known.
Replacement brought forward
Cousins had planned to retire from the catering company on 31 March after 11 years in the role. His replacement, Dominic Blakemore, was to take over on April 1 but his appointment has been brought forward to January 1. Blakemore was promoted from chief operating officer of the company's Europe division.
During his tenure, he led the firm back from the brink with shares recording a seven-fold increase and shareholders receiving £9bn in dividends and share buybacks.
"It has been a great privilege to know Richard personally and to work with him for the last few years,” Walsh said.
“Richard was known and respected for his great humanity and a no-nonsense style that transformed Compass into one of Britain's leading companies.”