Mark Turley, the director of services for communities at Edinburgh City Council, said that while he does not believe he personally contributed to any wrong doing, he feels it is right to do the "honourable thing".
It emerged in December 2012 that the council-run crematorium had buried or scattered the ashes of stillborn and newborn babies for decades without their relatives' knowledge. Parents were instead told there would be no ashes left to scatter following cremation.
In April this year, former Lord Advocate Dame Elish Angiolini said many parents face a ''lifetime of uncertainty'' about their child's final resting place after she conducted a year-long inquiry into the crematorium's practices from 1967 to 2011.
She was appointed by the council to head an investigation and she set out 22 recommendations for the local authority and other agencies to pursue in the wake of the scandal.
In her final report, which centred around the cases of more than 250 babies, she concluded the situation was a ''great tragedy''.
In a statement released today, Mr Turley said: "Whilst I do not believe I personally contributed to any wrong doing at Mortonhall Crematorium, as the director with ultimate accountability I believe it is right that I do the honourable thing in recognition of working practices at Mortonhall as criticised in Dame Elish Angiolini's recent report. I have therefore asked the chief executive to accept my resignation.
"I would like to thank the many partners and colleagues who have supported me through this difficult period and wish them all well for the future."
Council chief executive Sue Bruce said: "Mark has made a significant contribution to this council and to the city over the past 20 years, in particular in relation to the provision of housing. I respect the decision he has taken in these difficult circumstances.
"Following the media coverage of this issue I would like to take this opportunity to make it clear that Mark was placed under precautionary suspension to allow an investigation to take place. This is standard practice in such circumstances. In light of Mark's decision, that investigation will not now proceed.
"Mark leaves with our best wishes for the future."