Founder and business owner Paul Smith will continue to run the business, under Millington Travel’s ownership.
It comes after insolvency practitioner Begbies Traynor was appointed by Quartz in August.
A Begbies Traynor spokesperson said at the time: "Begbies Traynor in York has been instructed to assist the director of the business in seeking the appointment of administrators and a notice of intention to appoint administrators has been filed at court. Once appointed, the administrators will explore the potential sale of the business and assets.
"The company’s financial difficulties have arisen from a dispute with its managed services provider, through which holidays were booked, and resultant court proceedings.”
Millington Travel’s co-owner Nigel Armitage said: “Quartz is a robust business with a strong brand and a solid customer base.
“It has a great reputation locally in York and there are clear synergies between the two brands of Millington and Quartz. It’s a great fit.”
Smith added: “Joining the Millington team is great for us at Quartz Travel. We share a very similar working culture and the team here is delighted to have strong ownership for the future.”
Millington Travel has plans to continue to further develop its network.