The huge global oil and gas firm said the scheme, which will support the costs of living for students, would initially be worth £450,000 and provide 90 scholarships each worth £5,000.
The aim is then to expand and create an annual scholarship programme providing funding of up to £1.8 million a year.
BP has previously had a notable connection with higher education: its former chief executive, Lord Browne of Madingley, led the government's review into fees and funding in 2010.
Emma Judge, head of graduate resourcing at BP, said the firm had "reviewed and revived" its existing scholarship programme "in light of the changing circumstances students are now finding themselves in".
She also said BP wanted to address the "ongoing need to encourage students to study STEM subjects at university".
The aim was to get "great students studying subjects that are really valuable at some great universities", she added.
Applicants for the scholarships will go through an assessment process involving an application form, online psychometrics tests and an interview, Ms Judge said.
There was "no commitment" for those successful in winning funding to join BP after graduation, she said.
BP Scholars will be invited to participate in a range of activities both on campus and on site with the company.
"These will include a two to three-day interactive event designed to help students understand more about the oil and gas industry, with the opportunity to shadow a BP intern for two to three days during the summer, as well as early access to apply for both the BP internship programme and graduate programme," the firm said.
Ms Judge said the institutions involved in the scheme were chosen because they were "universities that we've got this great relationship with and where we've hired some great students from in the past".