(Reuters) - Cosmetics maker Avon Products Inc (>> Avon Products, Inc.) has agreed to give Barington Capital Group LP the right to approve the appointment of an independent director, in a bid to avoid a proxy fight with the activist investor.

The nominee would have to be jointly selected by Avon and its top investor, Cerberus Capital Management, to whom Avon sold a majority of its North America business earlier this month.

"We are pleased to have reached this settlement agreement with Barington, which allows us to avoid a potential proxy contest," said Chan Galbato, Avon's non-executive chairman.

The Barington Capital-led group has also agreed to withdraw its nominations for the Avon board elections to be held during the annual shareholder meeting scheduled for May 26.

Under the deal, Barington would vote in favor of all Avon nominees at the meeting. However, in the absence of a standstill agreement, Barington is not prohibited from agitating against the company in other matters.

The group, which owns more than 3 percent of Avon, had proposed a restructuring of the company in December, calling the appointment of Sheri McCoy as CEO a "mistake".

Avon has been struggling to reverse a steady decline in sales as the 130-year old pioneer of direct-selling loses favor to bigger players such as Estee Lauder Cos Inc (>> Estee Lauder Companies Inc) and other more exclusive brands, triggering discontent among its investors.

Avon said earlier this month it would cut 2,500 jobs and shift its headquarters to the UK, to which Barington said there was "still much more that needed to be done to improve the business".

Avon replaced half of its board when it agreed to sell a 19 percent stake to Cerberus Capital in December, adding three Cerberus executives to its board, including Galbato as non-executive chairman.

Shares of Avon, which named former FedEx Corp (>> FedEx Corporation) executive Cathy Ross to its board on Monday, rose as much as 9.1 percent to $4.67.

(Reporting by Yashaswini Swamynathan in Bengaluru; Editing by Shounak Dasgupta and Anupama Dwivedi)