The petition was organised in protest at his move to Goldman Sachs, where the former Portuguese Prime Minister is expected to advise the bank's clients on the Brexit fallout.
On Thursday, petition organisers told this website that so far, 62,000 people had signed the petition, which will run until the end of this month.
Campaigners say the case highlights the "revolving door" problem where top EU officials take up lucrative jobs in the private sector soon after stepping down.
Barroso started at Goldman Sachs, the American investment bank which was criticised for its role in the Greek economic crisis, in July.
Former European Commissioners must inform the Commission of any new position for up to 18 months after they leave office. Barroso's appointment came 20 months after he stepped down as Commission President, a role he served for two successive terms.
Theresa Crysmann, of the Brussels-based group Corporate Europe Observatory, said, "Many of the signees have expressed outrage at Barroso's appointment. There is a feeling that there is one rule for the political elite and another for the rest of us."
She said people from both the EU community and "others from all over Europe and different backgrounds" had signed the petition. People from the UK and Germany had been particularly prominent in signing.
Dutch GUE/NGL group MEP Dennis de Jong, who signed the petition, said, "As co-Chair of Parliament's intergroup on transparency, the 'revolving doors' issue is one of my key priorities.
"If under the current rules, Barroso's move to Goldman Sachs may [have been] found not to be illegal, that only shows that the rules are not watertight enough."
Another petitioner wrote, "Goldman Sachs, a banking corporation with a central role in causing the 2008 financial crisis, just found an easy way to make sure the EU operates in its interests.
"Barroso gained great political influence, contacts and insider know-how through his public post, all of which he could now use to benefit one of the most controversial financial corporations, which is already spending over a million euros in influencing the EU.
"This is a clear signal that our European institutions allow banks and big businesses to set the agenda."
The petitioner went on, "We need strong rules to prevent this, and sanctions if the rules are broken. Already the French President, dozens of members of the European Parliament and disgruntled EU staff have openly voiced their criticism, but the Commission remains silent despite the number of revolving door cases continuously increasing.
"A big community of Europeans shouting with one voice will surely help to kick it into action."
The petition is a partnership between the Alliance for Lobbying Transparency and Ethics Regulation (ALTER-EU) and Transparency International (EU Office).
Both plan to present the petition to EU political leaders at the end of this month and the case referred to the European Court of Justice.
A Commission source pointed out that Barroso had not broken any rules.