Ocheni is the new Minister of State for Employment, Labour and Productivity, while Hassan is the new Minister of Environment.
As was announced by his spokesman, Laolu Akande, late Tuesday night, the duo were sworn in at the Presidential Villa before the commencement of the weekly Federal Executive Council (FEC) meeting.
Their portfolios have not yet been announced, but Ocheni is expected to replace the late Minister of State for Employment, Labour and Productivity, James Ocholi, who died in an auto-crash in 2016, while Hassan takes the place of Amina Mohammed who resigned as Minister of Environment to take up the job of Deputy Secretary-General of the United Nations.
While addressing the ministers at the ceremony, Osinbajo asked them to serve with integrity and help the administration in its bid to rejuvenate the country's economy.
He said, "We have focused our intention on key areas of that economic reform programme and those key areas have become really what we believed need to be done to make a difference in the Nigerian economic and in the life and livelihoods of Nigerians.
"So, we expect that our new ministers will also join in this herculean task of turning around the Nigerian economy and making life better for the citizens of this country.
"You know aside from economy we have two major areas which of course as you know were highlighted by the president during the course of the campaign and after and have become the centrepieces of our administration’s programmes.
"Security and anti-corruption being the other two aside from the economy and we expect of course members of the Executive Council to focus on these key areas as well."
He continued, "And also our conducts should be exemplary so that we are able to show by practice not just by words that we are determined to ensure that this country is where there is good governance and where there is honesty and integrity in service to the people.
"Even as I welcome you to this cabinet, I congratulate friends and family who are here and I can only say going by your antecedents as contained in your resume read out, it is evident that you are deserving of positions held in the Federal Republic of Nigeria and that you are capable of rendering all the task that will given to you.
"The only reward is more hard work and I wish you the best as ministers of the Federal Republic of Nigeria."
The new ministers were confirmed by the Senate as far back as May 3, and the presidency's reluctance to promptly inaugurate them fueled talks of a cabinet reshuffle.
When Osinbajo travelled to meet the ailing President Muhammadu Buhari in London two weeks ago, the inauguration of the two ministers were reported to be one of the topics of discussion.