The scheme, totalling £100,000, will benefit 10 students beginning their master's degree this term.
It forms part of the legacy left by Sir Eric, who led the University for 14 years before he stepped down last year.
The ‘Professor Sir Eric Thomas Bursaries’ primarily target final-year undergraduate students who have been part of the Access to Bristol outreach programme – an initiative designed to encourage local pupils from a variety of backgrounds to study at university – and who plan to undertake a one-year full-time postgraduate course.
It’s also open to students whose circumstances make their path through higher education more challenging, such as those who are carers, have a disability or were mature students at an undergraduate level.
The aim is to ensure that all students, regardless of their background, have the support they need to achieve their full academic potential.
Sir Eric met the 10 recipients at a special presentation event held in Royal Fort House.
He said: "It's a huge honour to have a bursary scheme set-up in my name, and to know that these students’ academic journey is continuing thanks to the generosity of Bristol's alumni and friends.
"Throughout my time at the University, the abilities and passion demonstrated by our students never failed to impress me. Schemes like this are vitally important to ensure that the most able students are nurtured and encouraged to fulfil their potential, whatever their circumstances might be."
One of the bursary recipients is Kate Reynolds, who is studying for a PhD in Disability Studies.
Kate said: “I am a carer to two children with learning disabilities. I am also the first person in my family to attend a university at undergraduate level, as a mature student at University of Bristol. This bursary has been instrumental in allowing me to progress to postgraduate studies on a full-time basis. Without Sir Eric's bursary, I would have had to study on a part-time basis over six to seven years and start in the next academic year, both of which would have made me reconsider the possibility of studying a PhD at all. The bursary has been essential to my personal and professional development. I am extremely grateful for this opportunity.”