Heavy criticism has been aimed at Barroso, the former Portuguese premier for taking the Brexit-linked London job at the U.S. bank, 20 months after stepping down as Commission President.
Barroso faces a growing clamour for his generous EU pension to be removed after he moved to a senior job at Goldman Sachs.
He will soon take up a post at the investment bank's London headquarters as non-executive chairman of international operations and adviser, to "help it limit the negative effects of Brexit."
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An open petition has now been launched by staff in EU institutions demanding "strong exemplary measures" against Barroso, whose conduct "dishonours the European civil service and the EU."
The letter, by employees in the Commission, Parliament and Council, is highly critical of Barroso and calls for his pension to be withdrawn.
Separately, transparency campaigners have called for a minimum three-year ban for any European Commissioner on taking up new roles which risk a conflict of interest or involve any lobbying activity.
They also want the establishment of a fully independent and transparent ethics committee with the power to investigate and decide upon ex-EU officials' career moves, and to sanction them if rules are broken.
The petitioners are also calling for Barroso's entitlement to a generous Commission pension to be removed.
The European Ombudsman, Emily O'Reilly, has called for the EU to tighten rules on Commissioners taking appointments on leaving office.
O'Reilly said adhering to technical rules did not absolve former staff of a wider duty to show "integrity".
"The EU treaty states that former Commissioners should behave with integrity and discretion when it comes to certain appointments or benefits," the standards watchdog said, noting a "cooling off" period of 18 months when ex-Commissioners must seek clearance for new jobs to avoid conflicts of interest.
"Any suggestion that the spirit of the law is being ignored risks undermining public trust in the EU," O'Reilly added.
The Goldman Sachs employment of Barroso was condemned by the Alliance for Lobbying Transparency and Ethics Regulation (ALTER-EU) and European campaigning organisation WeMove.
A statement said, "Barroso has placed the EU's revolving door problem firmly on the political agenda. Although many former European Commissioners have taken up compromising roles with big business before, this is the first revolving door scandal involving an ex-Commission President, a development that has angered citizens, NGOs, EU governments and staff at the EU institutions alike.
"To keep up public pressure and ensure that the European Commission responds to the public outcry by sorting out its revolving door problem once and for all, we have launched a petition calling for stricter regulation of ex-EU officials' career moves once they've left office."
ALTER-EU, Corporate Europe Observatory's transparency campaigner Vicky Cann said: "Barroso has really surpassed previous revolving door scandals by joining a bank that is so controversial, considering its role in the 2008 financial crisis and its lobbying against EU financial regulation.
"No wonder that citizens, MEPs, the French government and EU institution staff have found this so hard to stomach.
"The EU's revolving door really undermines public interest decision-making. Former EU top dogs may no longer be working in politics, but they know the EU institutions inside out and will know exactly which strings to pull in favour of their new bosses."
Olga Vuković, of the campaigning organisation WeMove, said: "It is high-time for stricter rules to regulate post-Commission careers. So far, the European Commission's response to Barroso joining one of the most controversial financial institutions, and other cases like it, has been very disappointing."
Since May 2016 (when the period during which ex-Commissioners were obliged to seek authorisation for new roles ended), several Barroso II Commissioners have moved into "controversial" new roles in corporations or other organisations with links to big business. These new roles were all authorised by the Commission.
Apart from Barroso moving to Goldman Sachs, former trade Commissioner Karel De Gucht joined the board of mining giant Arcelor Mittal, and former digital agenda Commissioner Neelie Kroes has joined the boards of tech firms Uber and Salesforce.