Mark Turley, the director of services for communities at Edinburgh City Council, said that while he did not believe he personally contributed to any wrongdoing, he felt it was right to do the "honourable thing" following a critical report by Former Lord Advocate Dame Elish Angiolini.
He had earlier been suspended while an internal investigation was carried out into the council-run crematorium, where the ashes of stillborn or newborn babies were buried or scattered for decades without their relatives' knowledge. Parents were instead told there would be no ashes left to scatter following cremation.
Dorothy Maitland, a parent and bereavement charity worker who campaigned over the scandal, said she was saddened by his resignation, which she said was not the object of the campaign.
Ms Maitland, of the organisation Sands Lothian, said she was told in 1986 by staff at Mortonhall Crematorium there would be no remains of her daughter Kaelen, who had lived for just nine days.
She said yesterday: "I am saddened someone has to resign over Mortonhall, that was never the intention of our campaign.
"I can understand he was confident things were getting done properly, I thought that was happening as well. It's regretful he has to step down from his position."
In April this year, Dame Elish 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 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 on the cases of more than 250 babies, she concluded the situation was a "great tragedy".
Mr Turley was suspended by the council a week after the report was published, with the local authority saying the action had been taken pending an internal investigation.
In a statement, Mr Turley said: "Whilst I do not believe I personally contributed to any wrongdoing at Mortonhall Crematorium, as the director with ultimate accountability I believe it is right 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 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."
Thompsons Solicitors, who represent many of the families, has said lessons still need to be learned after the scandal.
Mr Turley's remit also included the axed housing repairs department and Liberton High School, where 12-year-old Keane Wallis-Bennett was killed when a changing room wall fell on her.