Olga Roche, the disgraced former child welfare chief ousted in April amid a firestorm of criticism, quietly retired as a state employee last Friday — right after she turned 60 — scoring a potentially hefty pension bump in the process, the Herald has learned.

Roche managed to stay on the state payroll at her $137,700 commissioner’s salary for nearly six months after her ouster, first as an “adviser” and then on family medical leave.

Her long goodbye raised the eyebrows and ire of state watchdogs.

“There was no question that she needed to go and she deserved to be fired. And now she’s made lemonade out of her failure to do her job,” said David Tuerck of the Beacon Hill Institute, a conservative think tank.

“We can only suspect the consulting opportunity was made to bolster her pension, and it’s shameful that state government turns itself into a welfare system for incompetent administrators,” Tuerck said.

Roche came under fire when a 5-year-old Fitchburg boy, Jeremiah Oliver, went missing for months while under the Department of Children and Families’ watch, before he was found dead, the first of several high-profile deaths of children under state care.

She filed for retirement in early August, shortly after she was slated to wrap up what officials described in the spring as a three-month stint as an adviser.

But she didn’t peg her final day until Oct. 17, according to a pension application obtained by the Herald — 10 days after her 60th birthday and nearly six months after formally resigning April 29.

The formula the state uses to calculate employees’ pensions factors in their average salary of the three highest consecutive years of service and age. By retiring at 60, instead of 59, Roche locked in a higher rate, likely earning her thousands more each year in pension pay.

A spokesman for the state Retirement Board said it was premature to calculate Roche’s pension until DCF provided her pay history, which the panel did not possess as of yesterday. But Gregory Sullivan, a former state inspector general, estimated that Roche’s extended stay could add an estimated $7,000 to her pension, boosting it to roughly $82,000 a year — based on her publicly available salaries and her 32-plus years of service.

“Gov. (Deval) Patrick is very loyal to his appointees generally, particularly so with Olga Roche,” said Sullivan, now of the Pioneer Institute. “He stuck with her until it was impossible to do any longer. Apparently, part of the arrangement was to allow her to remain on, on the same salary, until her birthday.”

In a brief phone interview yesterday, Roche confirmed she retired on Friday, and referred to a statement she released earlier through a state spokesman.

Asked if she stayed on the state payroll after resigning to increase her retirement pay, she said flatly, “No, sir,” before hanging up.

Alec Loftus, a spokesman for Health and Human Services, did not return repeated calls and emails, saying in a statement only that Roche has retired “and we will of course respect her request for privacy.”