Abolitionist and medic James McCune Smith graduated with an MD in 1837.
The James McCune Smith Learning Hub will open in the next academic year and is the first new building being delivered through a £1 billion campus development programme.
It comes as the university aims to provide “reparative justice” because of its historical links with the slave trade.
Professor Sir Anton Muscatelli, principal and vice-chancellor, said: “James McCune Smith was truly a pioneer, not only becoming the first African American to gain a medical degree, but also one of the leading intellectuals of his time.
“The University of Glasgow is proud of our association with his legacy and it is fitting that we honour it.
“The new James McCune Smith Learning Hub will revolutionise how we deliver learning and teaching support and provide a world-class facility for generations of future students from around the world.
“This is also consistent with actions agreed in our recent report, to provide reparative justice due to the university’s historical links with racial slavery, and emphasises our commitment to that programme.”