O'Day, now head of Roche's pharmaceuticals business, joined the company in 1987 and held various roles in the United States before moving in 1998 to headquarters in Basel, Switzerland.
O'Day's hiring comes about four months after Gilead said in July that Chief Executive John Milligan and Chairman John Martin would step down at the end of the year.
Jefferies analysts said in a note that O'Day's three decades of oncology and global commercial expertise at Roche should help Gilead build out its own global presence, particularly in new areas it is entering including oncology and inflammation as well as through more acquisitions and in-licensing deals.
At Roche, O'Day was a champion of bi-specific antibodies that are under development as a potentially less expensive, less complicated alternative to CAR-T therapy where T cells must be taken out of the body, re-engineered and re-infused.
With Gilead's Yescarta therapy, O'Day is now on the opposite side of the divide.
Separately, Roche said William Anderson, current CEO of its Genentech business, would replace O'Day next year.
Anderson joined Roche in 2006, leading the immunology business unit in Genentech, and then took charge of oncology sales and marketing. In 2013, he became head of global product strategy based in Basel before assuming his current role at Genentech in 2017.
Vontobel analyst Stefan Schneider called Anderson a "seasoned Roche manager" who played a key role in leading multiple sclerosis drug Ocrevus to success and driving double-digit growth in the U.S. market.
Gilead said on Monday that Martin would step down from the company's board of directors, effective March 1, 2019.
Up to Friday's close, the company's shares have fallen nearly 14 percent since Milligan and Martin's departures were announced by Gilead in July.
The Wall street Journal first reported O'Day's hiring on Sunday.
Gilead said its board had appointed Gregg Alton as interim chief executive for the period of January 1, 2019 until O'Day's start date of March 1, 2019.
Roche shares were down 0.6 percent by mid-morning, in line with the Stoxx European health care sector index.
(Reporting by Liana Baker in New York; Additional reporting by Ismail Shakil and Philip George in Bengaluru and by John Miller and Michael Shields in Zurich; Editing by Sunil Nair and Mark Potter)