African Union welcomed the statement from the rebels as the Ethiopian government had previously announced readiness for peace talks.
Ethiopia's Tigray rebels have said they were ready for a ceasefire and would accept a peace process led by the African Union, removing an obstacle to negotiations with the government to end almost two years of brutal warfare.
Sunday's announcement was made amid a flurry of international diplomacy after fighting flared last month for the first time in several months in northern Ethiopia, torpedoing a humanitarian truce.
"The government of Tigray is prepared to participate in a robust peace process under the auspices of the African Union," said a statement by the Tigrayan authorities.
"Furthermore, we are ready to abide by an immediate and mutually agreed cessation of hostilities in order to create a conducive atmosphere."
The Ethiopian government has previously said it was ready for unconditional talks "anytime, anywhere," brokered by the Addis Ababa-headquartered AU.
The Tigray People's Liberation Front (TPLF) had until now vehemently opposed the role of the AU's Horn of Africa envoy Olusegun Obasanjo, protesting at his "proximity" to Ethiopian Prime Minister Abiy Ahmed.
The TPLF statement, which coincided with Ethiopia's new year, made no mention of preconditions, although it said the Tigrayans expected a "credible" peace process with "mutually acceptable" mediators as well as international observers.
African Union welcomes announcement
AU Commission chief Moussa Faki Mahamat issued a statement welcoming the development as a "unique opportunity towards the restoration of peace" and urged "both parties to urgently work towards an immediate ceasefire, engage in direct talks".
Taye Dendea, Ethiopia's state minister for peace, described the TPLF announcement as a "nice development" on Twitter but insisted the "so-called TDF (Tigray Defence Forces) must be disarmed before peace talks start. Clear stand!"
The AU's Faki had held halks on Saturday with both Obasanjo, the former Nigerian president, and visiting US envoy for the Horn of Africa, Mike Hammer.
"May the parties in the conflict have the courage to choose talks over fighting, and participate in an African Union-led process that produces a lasting peace," Hammer said in a new year's message for Ethiopians on Sunday.
Fighting has raged on several fronts in northern Ethiopia since hostilities resumed on August 24, with both sides accusing the other of firing first and breaking a March truce.
The latest combat first broke out around Tigray's southeastern border but has since spread to areas west and north of the initial clashes, with the TPLF accusing Ethiopian and Eritrean forces of having launched a massive joint offensive on Tigray on September 1.
Untold numbers of civilians have been killed since the war erupted in Africa's second most populous country, and millions of people across northern Ethiopia are in need of emergency aid.