Jackett has previously been in charge of Watford and Swansea, leading the Welsh side to promotion from League Two in 2005 before narrowly missing out on a second successive promotion as the Swans lost the play-off final on penalties.
Jackett left Swansea by mutual consent in February and joined City in March, replacing Steve Wigley as reserves coach.
The 45-year-old had became a valued member of the Blues' coaching staff, leading the second string to a 3-1 victory over United to win this year's Manchester Senior Cup and helping out with the first team.
"We wish him good luck," Sven told the City website. "I'm sorry that we have lost him because he has been doing a great job since I came to the club.
"He's worked particularly well with the youngsters, and also helped us out with the first team when (assistant manager) Hans (Backe) was away. He goes with our best wishes and we wish him good luck for the future."