The 21-year-old, whose contract with Blues was due to run out in the summer, has signed a three-and-a-half year deal with the Super Lig outfit.
Elazigspor, who are based in the city of Elazığ, are currently in 16th spot in their 18-team division.
Jervis was signed up by Blues as a 15-year-old from Shrewsbury Town, but was unable to claim a regular first-team spot.
During his time at St. Andrew's, the Wolverhampton-born forward made five senior appearances for the club and failed to get on the scoresheet.
However, he spent numerous periods out on loan with a host of lower league clubs including: Hereford United, Notts County, Swindon Town, Preston North End, Carlisle United, Tranmere Rovers and most recently Portsmouth.
Blues boss Lee Clark said: "We wish Jake all the best and he’s got himself a great opportunity playing in the Turkish top flight.”