Peter Nutting said the council would ensure its new headquarters in Pride Hill as well as any other new office buildings across the county would have a flagpole in order to “proudly” fly the national flag every day.
Councillor Nutting said: “I have had a discussion with the chief executive, Andy Begley, to make sure all our public buildings that have got a flag pole do fly the Union flag.
“As we are arranging council buildings we are intending to make sure that all new buildings have flag poles, as well as existing ones."
Councillor Nutting said that while the guidance issued last week by the Department for Digital, Culture, Media and Sport did not apply to local authorities, he was keen for the council to follow the Government’s lead.
The new rules come into effect later in the year, replacing current guidelines which require it to be flown only on designated days.
Local Government Secretary Robert Jenrick said he would encourage councils to adopt the policy following the publication of the new guidance.
Mr Jenrick said: “Our nation’s flag is a symbol of liberty, unity and freedom that creates a shared sense of civic pride.
“People rightly expect to see the Union flag flying high on civic and Government buildings up and down the country, as a sign of our local and national identity.
“That’s why I am calling on all local councils to fly the Union flag on their buildings – and today’s guidance will enable them to do that.
“We’ve also cut red tape, allowing councils to also fly their county flag at the same time.”
Telford & Wrekin Council has flown the Union Jack at its headquarters for several years.
The authority's leader Councillor Shaun Davies said he welcomed plans from other councils to do the same.
He said: "Telford and Wrekin Council have flown the Union Jack and St George’s flag over our head office since we moved to the building in 2012, and we’ve done so before that for many years at previous head offices.
“I’m also aware many local town councils such as Great Dawley Town Council do the same.
“I’m glad that the government and other councils have followed our lead.”