Black replaces Paul Clement, who recently joined the coaching staff of Paris Saint-Germain.
"I am delighted that Eric has agreed to come on board," Kean told the club's official website. "He is someone with extensive coaching experience at the highest level and I feel sure he will play a key role over the coming months."
Black has previous coaching experience at Birmingham City, Wigan Athletic and Sunderland.
Rovers are currently 17th in the Premier League table.