The management and board changes follow the retirement of non-exec chairman Richard Stone.
Kennedy has been the company’s managing director since January, following Phil Parnell’s move from CEO to executive chairman.
From January 2012, Kennedy will assume the role of CEO and Parnell will move to non-executive chairman.
Parnell said: “Michael has played a significant role in the revival of Drambuie's fortunes in the past six years and is ideally placed to take the business forward over the next phase of its development.”
O’Neill, who formerly worked for United Distillers and Guinness Brewing, has joined as a non-executive director.
He will have responsibility for the audit and remuneration committees, in addition to his board responsibilities.
Parnell said: “With Richard Stone’s retirement earlier this year, it was important to bring an independent non-executive director onto the board and we are very pleased to be able to attract such a high-calibre individual such as Brendan O’Neill to Drambuie."
Brown, who has been with the company since 1994, has been appointed director of Drambuie.
Previously, he operated as regional sales director for northern and eastern Europe but also had a stint managing Drambuie’s Japanese and South Korean business.
Parnell added: “In Jonathan we have a terrific brand ambassador who is passionate about Drambuie and who ably represents the brand at home and abroad.”