Professor Neil will succeed Muriel Robinson, who will retire in April after 10 years at the 150-year-old former Anglican teacher training college, which is based in Lincoln.
He is currently interim executive dean of the faculty of education, health and social sciences at the University of the West of Scotland, and has also held positions at Queen's University Belfast and Aberystwyth University.
The educationalist and theologian, who will take up his new position in May, said: "I have followed the progress of this gem of an institution for many years and I very much look forward to working with the staff and students through the next phase in its development."
Haydn Beeken, chair of Bishop Grosseteste's university council, said Professor Neil "stood out amongst a strong field of candidates for his academic and leadership track record", and had displayed a "passion" for the institution's "ethos".
Bishop Grosseteste was part of what universities and science minister David Willetts termed "the biggest creation of universities since 1992" when, alongside nine other small specialist institutions, it benefited from the government's lowering of the student number threshold for university title from 4,000 to 1,000.
Meanwhile, Royal Northern College of Music vice-principal Linda Merrick has officially taken on the top job after functioning as acting principal since July 2012.
The clarinettist described the 40-year-old institution as "a very special place".
"Recognised as one of the world's leading conservatoires and one of the busiest and most forward-looking public arts venues in the UK, it holds a unique position in the cultural life of the Manchester and the wider north-west region," she said.
The chair of the college's board of governors, Nick Prettejohn, said: "Linda's musicality, leadership and energy provide just the right qualities to consolidate and grow our position."
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