The official confirmation comes a day after Chad denied accusations that it had launched a series of air strikes on Sudanese territory on Saturday.
Younousmi said Chad forces had cleared out all rebel bases up to 40km inside Sudan and destroyed seven regrouping points, while "the fugitives have been dealt with by the air force with no collateral damage".
The Union of Forces for the Resistance (UFR), a coalition of rebel factions based in Sudan, launched an offensive on May 4 with the stated goal of taking Ndjamena.
But Chad's army counter-attacked and by May 10 was claiming victory, with Idriss Deby Itno, the president of Chad, vowing on Saturday to wipe out the rebels and "pursuing" them into foreign territories if necessary.
"We have used our right to pursue and that right to pursue will continue with the support of the Chadian people," Deby said.
"The army has decided to finish once and for all with the mercenaries in the pay of Sudan."
Both countries have regularly accused each other of backing fighters bent on overthrowing their respective governments.
Call for calm
Haile Menkerios, the UN deputy secretary-general, urged Chad to take the diplomatic path.
'The Chadian government should start negotiations with the Chadian rebels, that should happen," Menkerios told the AFP news agency in Addis Ababa.
"There should be a peaceful resolution of the issue between the two countries."
Last week Chad accused Sudan of sponsoring the rebels' advance – a charge denied by Khartoum – after the two countries had signed a pact in Doha, Qatar.
They had agreed in that deal to normalise relations and reject any support for rebel groups hostile to either of them.
Chad said it had stopped the advance, after clashes that killed 125 fighters.
Sudan denied involvement in the raid, saying it was a confrontation between Chad's government and "opposition groups".
Chad and Sudan resumed shaky diplomatic ties in November after cutting them in May 2008.
Sudan has accused Deby of being involved in an attack on the Sudanese capital by Darfur rebels on May 11, 2008.
Eastern Chad is a temporary home to about 300,000 refugees who have fled Sudan's Darfur conflict. The region also has camps for 187,000 Chadians displaced by fighting locally and in Darfur.