In brief updates to the London Stock Exchange, both companies said she would be leaving the roles, which include responsibilities for setting executive pay and upholding corporate responsibility.
She took home £89,000 in fees from Morrisons and £30,000 from Dunelm in the past year, according to the latest published annual accounts.
Dunelm chairman Andy Harrison said: “We respect Paula’s decision to step down from the board and I would like to thank her for the positive contribution she has made to the business since her appointment in September 2019.”
Morrisons chairman Andrew Higginson said: “Paula has been an insightful, effective and hardworking non-executive director, and, on behalf of the board, I want to thank her for her significant contribution over the last five years.”
The moves came as the former Post Office boss said she is “truly sorry” for the “suffering” caused to subpostmasters who were wrongly convicted of offences.
Ms Vennells, who is an associate minister in the Diocese of St Albans, issued the apology on Sunday as she announced that she would be stepping back from her regular church duties in the wake of the Horizon scandal.
Hundreds of subpostmasters were prosecuted for theft, fraud and false accounting because of the Post Office’s defective Horizon accounting system, which had “bugs, defects and errors” from the very outset.
On Friday, 39 former subpostmasters who were convicted and even jailed based on Horizon data had their convictions overturned by the Court of Appeal.
Ms Vennells, who was Post Office chief executive from 2012 to 2019, said she would be stepping back from her regular parochial duties following the ruling.
Ms Vennells, who was made a CBE for “services to the Post Office and to charity” is an associate minister in Bromham, Oakley and Stagsden, Bedfordshire.
The diocese said she had informed the Bishop of St Albans, the Rt Rev Alan Smith, who is the son of a former postmaster.
In a statement, Ms Vennells said: “I am truly sorry for the suffering caused to the 39 subpostmasters as a result of their convictions which were overturned last week.
“It is obvious that my involvement with the Post Office has become a distraction from the good work undertaken in the Diocese of St Albans and in the parishes I serve.
“I have therefore stepped back with immediate effect from regular parish ministry, and intend to focus fully on working with the ongoing Government inquiry to ensure the affected subpostmasters and wider public get the answers they deserve.”
The Bishop of St Albans said it is “right” that Ms Vennells “stands back from public ministry” following the ruling.
He said: “As the son of a former subpostmaster I express my distress at the miscarriage of justice that so many subpostmasters have suffered.
“They and their families are in my thoughts and prayers. I am glad that these and earlier appeals have overturned convictions that have been found to be unjust.”
Ms Vennells left the Post Office in 2019, months before a damning High Court judgment in a civil claim brought against it by hundreds of former subpostmasters.
The Post Office knew there were “serious issues about the reliability” of the Fujitsu-developed IT system, which was rolled out to branches in 2000, but continued to bring “serious criminal charges against the subpostmasters on the basis of Horizon data”, the Court of Appeal said on Friday.
Lord Justice Holroyde said the Post Office “effectively steamrolled over any subpostmaster who sought to challenge its accuracy”.
Three of the former subpostmasters, Wendy Cousins, Stanley Fell and Neelam Hussain, had their appeals dismissed by the court because “the reliability of Horizon data was not essential to the prosecution case”.
After the ruling was delivered at the Royal Courts of Justice in London, former subpostmasters whose convictions were overturned called for a public inquiry into the scandal which “destroyed” people’s lives.
The Criminal Cases Review Commission, which investigates potential miscarriages of justice, has encouraged any other former Post Office employees to consider challenging their convictions following the ruling.
Post Office chief executive Nick Read said: “The quashing of historical convictions is a vital milestone in fully and properly addressing the past as I work to put right these wrongs as swiftly as possible, and there must be compensation that reflects what has happened.”