Emily O'Reilly, the Strasbourg-based ombudsman, will be asked to investigate Barroso's move to US investment bank Goldman Sachs.
A parliamentary resolution asking her to launch a probe was overwhelmingly passed at the plenary in Strasbourg on Thursday by 557 votes to 24, with 44 abstentions.
The demand comes after the European Commission's ad-hoc ethical committee recently recommended that Barroso should not be reprimanded for joining Goldman Sachs. It said the former Portuguese Prime Minister did not breach EU treaties.
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However, a spokesperson for Corporate Europe Observatory, a Brussels based group campaigning for more transparency in EU affairs, said, "There is no question that Barroso must be sanctioned."
O'Reilly is already investigating the Commission's other revolving door cases in which former senior EU officials take private sector jobs in their fields of expertise soon after leaving their posts, which it is claimed may result in conflicts of interest.
MEPs, in the resolution adopted this week, cite Barroso's appointment last summer as non-executive chairman of the Goldman Sachs International investment bank, and called for an inquiry into the Commission's handling of the case.
They also say that particular attention needs to be paid when appointing candidates to positions in any EU institution.
Parliament's rapporteur on the issue, ECR group Greek member Notis Marias said, "This report raises several important issues which the Ombudsman has been dealing with in 2015 and which need further attention.
"We welcome her efforts for greater transparency, and urge her to push for more openness in order to safeguard the good administration and democratic accountability within the EU decision-making process."
The demand for a probe comes after MEPs discussed the ombudsman's annual report this week.
As in recent years, transparency-related issues top the ombudsman's list of 278 inquiries opened in 2015.
Parliament praised her "continued efforts" to increase openness within the TTIP talks and three-way informal negotiations on legislation between the European Commission, Parliament and Council.
MEPs also called on O'Reilly to push for "more clarity and good administration" within the European Central Bank.
The report drafted by Marias welcomes the fact that in 2015, all EU institutions introduced internal rules on whistleblowing.
His report adds, "Parliament nonetheless again stresses the need for an EU directive on whistleblowing, containing minimum appropriate guarantees and legal safeguards for people revealing illegal or unethical activities in the public or private sectors."
It also welcomed the Commission's recent proposal for a mandatory lobby register for all EU institutions, aimed at closing all loopholes concerning the activities of individuals and companies working on influencing EU decision-making.