Jones, who is also currently the chair of Hawksmoor and Mowgli, will join the recently listed company’s board of directors as the chair of the remuneration committee and as a member of the audit committee.
Reiniche, meanwhile, who is also a non-executive director of PayPal Luxembourg, will join as a member of the audit, remuneration and nominations committees.
"We are delighted to have brought on board Karen and Dominique who bring substantial expertise in the restaurant and food and drink sectors, as well as deep knowledge of consumer marketing and real insight into our European markets," says Claudia Arney, chair of Deliveroo.
"They join at an important time for Deliveroo as we build on the opportunities ahead of us as a public company. They will provide a valuable and fresh perspective to support the company's continued growth."
Reiniche will commence her appointment on 1 May, while Jones will join the board on 1 June.
"I am looking forward to working with the Board and the wider Executive team to build the business through strong and mutually beneficial partnerships with customers, riders, restaurants and food retailers to the benefit of all," says Jones, who founded Café Rouge with Roger Myers in 1989.
She was also previously CEO of Spirit Group.