The Prime Minister will announce a Green Paper on Monday that will launch work to develop and finalise the strategy in consultation with industry.
CBI director-general Carolyn Fairbairn said the final plan must focus on boosting flagging productivity and addressing regional imbalances.
She said: "A modern industrial strategy will be a landmark opportunity to build a successful, modern economy as the foundation for a prosperous, fairer and more inclusive society.
"It must help fix the country's productivity problems and remove the regional inequalities that have dogged our country for generations, having a positive impact on living standards, wages and the future opportunities of many people.
"The CBI has long-called for a new industrial strategy and it's welcome to see the Government creating an opportunity for all sectors to get involved."
The Federation of Small Businesses (FSB), which was involved in discussions leading to the Green Paper, welcomed the Government's move towards providing region-specific help for firms.
FSB national chairman Mike Cherry said: "We are proud to be influencing a major Government economic blueprint and particularly pleased with the push on skills, infrastructure and connectivity as important drivers of productivity and industry.
Business leaders have said the PM has a 'landmark opportunity' to improve Britain's economy
A modern industrial strategy will be a landmark opportunity to build a successful, modern economy
Carolyn Fairbairn, CBI director-general
"In addition, the moves towards a place-based strategy fit well with the UK small business community.
"Small firms are often the anchors in our local economies – in cities, towns and villages — right across the country."
Terry Scuoler, the chief executive of EEF, the manufacturers' organisation urged the Government to work together with "clear leadership" from the PM and Cabinet to make the strategy a success.
He said: "This is an important first step towards creating a comprehensive, consistent and long-term industrial strategy that will help Britain adjust to a more globally-focused, post-Brexit economy.
Carolyn Fairbairn said the final plan must focus on boosting flagging productivity
"Manufacturing has a key role to play and we look forward to working with the Government on crystallising this into a strategic framework that will work and deliver for industry.
"The end result of this process must be an industrial strategy that lives up to the promise of driving different behaviours and outcomes for the British economy."
British Chambers of Commerce director general Adam Marshall said: "The developing industrial strategy represents a crucial first milestone in a renewed partnership between business and government, working together to create the conditions for future growth.
"Business communities across the UK will be pleased to see that harnessing the potential of our cities, towns and counties lies at the heart of the Government's approach to industrial strategy.
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"There are dynamic business communities in every corner of the UK – and it is their future success that will make our country more competitive and more prosperous.
"A deliberate and steady approach that leads to long-term change is the right way to go."
The aerospace industry welcomed moves to create sector deals.
Paul Everitt, the chief executive of the aerospace trade body ADS says: "Sector specific industrial strategies are already helping UK aerospace to increase investment in R&T, improve productivity and compete more effectively in tough global markets.
The Prime Minister will announce a Green Paper on Monday
"Today's Green Paper signals a more ambitious approach to securing growth and preparing for the inevitable pressures that will accompany Brexit."
AstraZeneca, the pharmaceutical giant, said the Government must include transport links and housing in its strategy.
Pascal Soriot, the chief executive of the Cambridge-based firm, said: "Strategic support for the sector with the right incentives and policy environment is critical to maintaining our global competitiveness in developing, manufacturing and adopting medical innovations that benefit patients.
Mrs May will also finalise the strategy in consultation with industry
"As a long-standing investor in UK science and partnerships with academia, we believe the creation of vibrant geographic areas of excellence would truly catalyse discovery and innovation.
"Supported by transport and housing infrastructure that facilitate collaboration and attract the best talent, these clusters would boost the knowledge economy and anchor industrial activity throughout the UK."
This comes after the PM's talk on the Andrew Marr show on BBC.