Under the terms of the agreement, a Barington board member will have to be selected jointly by Avon and its top shareholder Cerberus Capital Management, which bought a majority stake in Avon's north American arm earlier this year.
In exchange, Barington has also agreed to withdraw its nominations for more board seats at its annual meeting in May and to vote all of its shares in favour of the nominees proposed by the Avon board.
Avon has also named former FedEx Corp executive Cathy Ross to its board, increase the number of members from nine to ten. Ross was chief financial officer at FedEx Express until last year.
Barington, which leads a group of investors that own more than three per cent of Avon’s shares, had called for a shake-up of Avon's management in December, arguing that a better leadership team could help boost the company's performance after years of weak sales.
In a letter to the group's former chairman Douglas Conant, who stepped down after the Cerberus acquisition, Barington cited a list of "chronic failures" including its rejection of a takeover offer by Coty and a poor choice of chief executive as the primary reasons for its poor share market performance.
The company has since announced it will cut about 2,500 jobs worldwide and shift its corporate headquarters from New York to the UK in a bid to turn itself around.
Barington's chairman and chief executive, James A. Mitarotonda, said: "We are pleased to have reached this agreement with Avon. We have spent time with Avon's management team and members of the board discussing our strategic and operational suggestions, and we are confident that Avon is taking the necessary actions to improve the long-term performance of the company."
Chan W. Galbato, Avon's non-executive chairman, said: "We are pleased to have reached this settlement agreement with Barington, which allows us to avoid a potential proxy contest. We have a process underway to identify the additional independent board member and we look forward to working with Barington to complete that process."