The reappointment of the two officers by the state government after their retirement had been challenged in court by a retired police officer, Rahul Sharma.
Mr Amin was rehired on contract as Superintendent of Police in the Tapi district and Mr Barot was a Deputy Superintendent of Police in the Railways.
The Supreme Court had said yesterday that the Gujarat government must take a call on the officers or it would pass orders.
After the strong observations of the judges including Chief Justice JS Khehar, the two officers pledged to resign in the course of the day.
Rahul Sharma, a former Indian Police Service (IPS) officer, had questioned the Gujarat government for re-appointing officers who faced serious charges.
His petition alleged that Mr Amin has faced trial in the Sohrabuddin Sheikh and Ishrat Jahan encounter killings and has spent close to eight years in jail but he was "immediately reinstated" after his release.
Mr Barot was accused in the Sadiq Jaman and Ishrat Jahan killings, was accused in two cases of abduction and murder and spent close to three years in jail, said the petition.
Appointments have been made despite "bearing in mind the questionable track record of the two officers", in violation of Supreme Court guidelines and "the doctrine of public trust", the petition said.
Earlier this year, another top officer accused in the Ishrat Jahan case, PP Pandey, was forced to resign as Director General of Police.
Ishrat Jahan and three others were killed in an alleged fake encounter in Gujarat in June 2004. The Gujarat Police said they were Lashkar terrorists and were in Gujarat to assassinate the then Chief Minister Narendra Modi.
A CBI court is hearing the Ishrat Jahan case. The CBI has filed two charge-sheets, the first of which accuses Gujarat police officers of staging a fake encounter to kill the four people.