They both said their defection is in accordance with the letters and spirit section 109 (1) (g) of the Constitution of the Federation Republic of Nigeria, 1999 as amended.
He said that the development of the transport sector by knowledge transfer and capacity building would generate employment opportunities for Nigerians.
Mr Buhari had rejected the legislation, saying in a democratic setting, parties should be allowed to choose their preferred mode of primary.
Senators-elect numbering 100 out of the 109 slots at the red chamber will be receiving their certificate of return.
His recent comment, wherein he opposed the restructuring, one of the demands of Southern State Governors in Nigeria, is said to have further emboldened his aggrieved antagonistic colleagues who are plotting his removal from office.
The letter announcing the stepping aside of the lawmakers was read on the floor of the house by the speaker, Francis Nwifuru, on Tuesday.
Mr Osinbajo declared interest in next year's race on Monday after meeting with state governors of the party Sunday night.
The two chambers at the National Assembly had recently passed the PIB but differed in their recommendations on the funds for host communities.