Number crunchers behind the project estimate landing the broadcaster would prove to be the catalyst for a major boom in the wider media sector over the next 10 years.
It would also boost the employment market as Channel 4 could bring some or all of their 700-strong workforce and it is possible new job roles could be created.
Creative Sheffield, the council's economic development function, is leading the bid and said the growth forecast is based on inward investment with the belief that more media companies would want to move to Sheffield to be closer to C4 commissioners.
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Meanwhile, existing firms - such as those who produce TV programmes and design graphics and effects - would win more contracts and be likely therefore to expand.
In addition, having C4 would attract more students to both universities and they would be more likely to stay in the city rather than find employment elsewhere.
Business and cultural leaders have today welcomed the £1bn forecast and described how landing the broadcaster would be a 'game changer' for the city's digital and media sector.
Mazher Iqbal, the council's cabinet member for business and investment, said: "We think Channel 4 and Sheffield are a great fit and we’ve used the bid document to demonstrate that.
"We’ve put Sheffield on the map and shouted about our city. “
Included in the bid was the Digital Report - a document pulled together by industry experts that concluded Sheffield's digital sector is on the cusp of huge growth.
Professor Vanessa Toulmin, director of city and cultural engagement at the University of Sheffield, helped to pull the report together and said landing C4 could unlock the city's potential.
She said: "The digital report demonstrates the wealth of creative talent that is latent in the city in some parts and trail blazing in others. Having the lynchpin of C4 could be a game changer."
Digital Report author Laura Bennett added: "What emerged from the creative digital report is that Sheffield is on the cusp of something big, and the arrival of C4 to the city would really help to propel us forward. It will bring jobs to our region, create a buzz, and lead to further opportunities."
The bid was submitted to the department for culture, media and sport last week and the Steel City faces stiff competition from Liverpool, the West Midlands, Bradford, Manchester and Cardiff, who are also understood to be campaigning for the broadcaster.
Richard Wright, executive director of Sheffield Chamber of Commerce, said: "We are in a competitive situation where only one place can succeed. That apart, we have a great offer and a city with many attributes that will be attractive to Channel 4.
“What is really pleasing to me is that we now have the confidence and ambition to go for this. It shows how far the city has come culturally and mentally."
The Government has said it will move the publicly-owned corporation out of its £100 million London headquarters to another base elsewhere in the UK to help drive creative jobs throughout the regions.
Project leaders have already earmarked a vacant site at Sheaf Square, near the railway station, as a possible home for the channel and initial artists' impressions have been drawn up.
Those leading the bid point to Sheffield's heritage as a creative force, such as being home to Warp Films, and its central location as major selling points.
Channel 4 bosses have expressed concern about the relocation and argued it would be costly to move out of the capital.
The Government has not yet revealed a timescale for processing the bids or what the next stage is.