Kraft will replace Martin Jarmond, who left to join UCLA on a six-year deal last month.
BC has been eyeing Kraft in large part due to his success maximizing Temple's football program alongside Matt Rhule from 2013-16. Rhule, who joined Baylor after the 2016 collegiate campaign, became the head coach of the Carolina Panthers this offseason.
The Eagles have significantly increased their investment in football following the hiring of head coach Jeff Hafley.
At Temple, Kraft helped lead the program to five straight bowl appearances from 2015-19 and its first conference title in 49 years in 2016.