African Union president and Senegalese President Macky Sall said it was "excellent news".
"I congratulate the parties and strongly encourage them to persevere on the path towards permanent peace," he said.
Neighboring Kenya's President William Ruto welcomed the news.
"I applaud (Ethiopian) Prime Minister Abiy Ahmed and the leadership of Tigray for their bold step towards restoring peace in Ethiopia," he said.
"This mutual agreement will create the necessary environment to nurture durable peace and political stability in Ethiopia."
The two warring sides announced a truce on November 2 after more than a week of closed-door peace discussions.
United Nations Secretary-General Antonio Guterres heralded the announcement as a "welcome first step" in ending the fighting.
"It is very much a welcome first step, which we hope can start to bring some solace to the millions of Ethiopian civilians that have really suffered during this conflict," UN spokesman Stephane Dujarric told reporters.
The European Union congratulated both sides "for their commitment and courage towards peace", but encouraged further talks to achieve "a permanent ceasefire agreement".
"A swift implementation on the ground of the agreement reached today is needed," it added.
"Priority is to resume humanitarian access in all affected areas and to restore basic services, in particular in Tigray."
British Foreign Secretary James Cleverly on Thursday said he welcomed an agreement between Ethiopia's government and rebel authorities in the Tigray region to end hostilities.
"I applaud their choice of peace, and the mediation efforts of African Union, South Africa and Kenya. UK is ready to support the peace process," he tweeted.
Observers say the truce comes as Ethiopian PM Abiy said his forces can press forward toward a "victory" over the Tigrayan TPLF, and note that Addis has captured a series of key Tigrayan towns in its recent thrust into that region.