The company, which brings together Ray-Ban maker Luxottica and lenses specialist Essilor, also reaffirmed its ambition to find a new chief executive by the end of 2020.
Shares in EssilorLuxottica, which have been rattled as the dispute was fought out in public, were up 0.27 percent at 1422 GMT, among the rare gainers on the Paris benchmark CAC-40 index, which was down 1.4 percent.
"The settlement allows a step forward in restoring a more constructive spirit between sides, (a) precondition to seize potential synergies of the merger," equity broker Equita wrote in a note to clients.
The merger parties were supposed to have equal weight in the combined group's leadership, but the French and Italian sides have increasingly accused each other of trying to dominate in recent months.
Tensions surfaced in November when Luxottica's founder, Leonardo Del Vecchio, who is chairman of the merged entity and its largest shareholder, appeared to tap his right-hand man and Luxottica chief executive Francesco Milleri, as the next CEO.
The battle culminated in March when Del Vecchio's holding company Delfin said it would seek arbitration in the International Chamber of Commerce, prompting Essilor to ask a Paris court to nominate an outside mediator.
EssilorLuxottica said in a statement on Monday that Del Vecchio and executive vice chairman Hubert Sagnieres had "empowered" Milleri and Laurent Vacherot, Essilor's current CEO, to focus on the integration process and define strategy.
As part of the agreement, neither Milleri nor Vacherot will apply for the future CEO role.
Vacherot was also appointed as a director of EssilorLuxottica to ensure the board keeps a strict balance between the two companies.
FOLLOW THE MONEY
EssilorLuxottica, now owner of a portfolio spanning brands including Oakley, Persol, Oliver Peoples and Varilux, is due to hold its annual shareholder meeting on Thursday, where some minority investors are expected to voice their frustration over the leadership row.
Some investors have also expressed concern that the leadership crisis might delay or scupper promised savings, at the very core of the proposed deal when presented in 2017.
Last week, however, the group confirmed 2019 targets, including a rise in sales of 3.5 to 5 percent, and pledged to deliver on planned synergies of up to 600 million euros annually in the next three to five years.
Before Monday's announcements, several minority shareholders including management companies Phitrust and Comgest, submitted resolutions to appoint additional independent directors at Thursday's annual meeting. EssilorLuxottica's board had advised shareholders to reject the proposals.
"It is very likely that we will maintain our submitted resolutions," Denis Branche, managing director with Phitrust told Reuters.
Valoptec, a group representing more than 10,000 former and active employees which had also been pushing for the nomination of an independent director, said on Monday it was withdrawing its resolution.
The association will join EssilorLuxottica's strategy and integration committee.
(Reporting by Matthias Blamont, Sudip Kar-Gupta in Paris ; Claudia Cristoferi in Milan ; Editing by Alexander Smith and Mark Potter)
By Matthias Blamont