Last year the Council sold Civic Centres 1 to 4 to Coventry University and the removal of the bridge link is the next step in this process.
The University has exciting plans for the site which will see it opened up and transformed gradually into a new headquarters and facilities for postgraduate work and international engagement.
The Council House will be restored to how it looked before the bridge link was installed in the 1970s.
A new window will be made and installed by a specialist contractor later this year, and it will be in keeping with the rest of the Council House. A temporary cover will be in place until the restoration work begins.
Martin Yardley, Deputy Chief Executive, said: “The Council House is, and will remain, the heart of our democratic decision making.
“It is an important piece of our heritage and it will be great for everyone to see it as it originally was."
Earl Street will be closed to traffic on Sunday 9 April while the work is carried out.