Gov. Pat Quinn added $10 million in state funding to bring the number of workers to nearly 2,000.
The school also has considered expanding its building on Loyola Avenue to stay in the neighborhood.
School, on academic probation 11 years, has had two principal changes in less than a year.
The renovations to Taft were "long overdue," said Chicago Public Schools CEO Barbara Byrd Bennett.
Dyett High School was scheduled to close at the end of the upcoming school year.
The school hired seven teachers to keep up with continued growth.
Local 134 of the International Brotherhood of Electrical Workers agreed to hire student graduates.
Construction preperations on the annex could begin as early as Monday.
Aldermen Mary O'Connor, Matt O'Shea and Marty Quinn said the policy "could be viewed as unfair."
The new alternative high school can accommodate up to 300 students and is tuition free.
Annexes at three CPS schools were approved Tuesday by the Public Building Commission.
More than 200 volunteers built the playground from the ground up.
CPS told Gale Elementary's principal it didn't include the school in a federal funding request.
For the second time this year, there is confusion at Earle Elementary over the principal's departure.
For the third time since December, Earle STEM Elementary School will have a new principal.
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