Tanzanian Health Minister Umy Mwalimu said that the doctors would be sent to Kenya "as soon as possible".
"We would also wish to know why this request has been made during the strike, and the implementation has to come a few days after the agreement to terminate the strike", read a statement sent to newsrooms.
On Friday, there were only two doctors on duty at the Kenyatta National Hospital, the biggest public hospital in the country, a nurse told a Reuters reporter.
The government offered no further information as to when the doctors would be deployed or how long they would stay in Kenya.
But Mailu said the 1,400 doctors said to be out of employment were on private practice by design.
Among the reasons for the Kenyan strike was the shortage of doctors in public hospitals in the country, in addition to pay.
But the move to bring doctors from foreign countries was opposed by Kakamega Governor Wycliffe Oparanya.
On concerns about going against Public Service Commission regulations on employing non-citizens when there are citizens with appropriate qualifications, the Health CS said: "We do not have the skills, even with doctors from the private sector, to address the shortage as all doctors are absorbed". Health CS Cleopa Mailu, PS Nicholas Muraguri, Council of Governors chair Peter Munya and KMPDU secretary general Ouma Oluga signed the deal.
"As you assure me that you will pay the required salaries to my doctors and give them housing, that they will work in good conditions, I have no problem", Magufuli said.
This comes just a week after the Medical Association of Tanzania President, Obadia Nyagole, said that the neighbouring country is facing a shortage of 1,794 doctors and, therefore, can not allow the country to export medics to Kenya.