The talks, known as the intra-Afghan dialog, will be the first high-level meeting between the two sides after years of fighting.
No date has been announced for the meeting, but it is expected to take place after the two sides settle differences on the release by the Afghan government of 5,000 Taliban prisoners, which could be as soon as the end of next week.
"The first intra-Afghan meeting will happen in Doha," Taliban spokesman Suhail Shaheen told Reuters, adding that the Islamist group was ready to hold intra-Afghan talks within a week of the release of 5,000 prisoners.
The Afghan government has released 3,000 Taliban prisoners so far under an agreement signed between the United States and the insurgent group in February.
That deal outlined a roadmap for withdrawing foreign forces from Afghanistan and peace talks to end the 19-year war.
The government wants talks to begin as soon as possible but has issues with the release of a few hundred high-profile Taliban prisoners, a senior government official told Reuters.
The official said the government had offered an alternative prisoner release list to the Taliban.
The spokesman for the Afghan Presidential Palace, Sediq Sediqqi, said on Twitter that Doha had been agreed as the venue for the first talks but said no permanent venue had been agreed.
The Qatari capital was the venue for signing the deal between the United States and Taliban. The insurgent group has had a political office in Doha since 2013.