Baradar, often described as the Taliban's former second-in-command, will be released tomorrow, Pakistan's foreign ministry in Islamabad said in a statement.
"We welcome that this step is being taken," Aimal Faizi, spokesman for Afghan president Hamid Karzai told AFP. "We believe this will help the Afghan peace process.
"This is something we have been calling for for a long time. It was on the agenda when the president visited Pakistan, so we are pleased."
During the visit, the Afghan president urged Pakistan to help arrange peace talks between his government and the Taliban.
Elements of the Pakistani state are widely accused of funding, controlling and sheltering the Taliban, but Islamabad says it will do anything to stop the fighting in Afghanistan.