The authority has already contacted 75 businesses throughout the borough, including 36 that have been directly affected, and will make the first payments on Friday.
About 150 businesses in Telford & Wrekin are thought to have been affected in some way by the floods and could qualify for financial aid.
A further 20 grants are expected to be paid out by the end of next week, to the tune of £30,000.
Councillor David Wright, cabinet member overseeing flood recovery, said: "It's vital we accelerate the support available to flood-affected businesses, which like many of our residents, are reeling from the effects of February's severe storms and flooding that have had such an effect on the borough.
"In the Ironbridge Gorge many of those affected are small businesses who can ill afford such disruption to their businesses.
#backtobusiness - how to take part
Let us know when your business is back in action after the floods
Let us know how people can help
Tell us about customers and residents who have gone above and beyond to help
We'll share the best stories with our readers and help Shropshire get back on its feet
TWITTER - use the hashtag #backtobusiness to share your stories with us
FACEBOOK - Visit our Facebook Community Noticeboard to share your stories
You can also share your stories using this form:
"That's why it's vital that we make these grants available now to help businesses recover and not wait for government funding to come through.
"We must do all we can to help and make it as easy as possible for businesses to get back up and running."
A government grant of up to £2,500 for small and medium sized businesses severely affected by flooding is available. Businesses which have been directly affected by floodwater or have suffered from a loss of trade as a result of flooding and cannot recover costs from insurance can apply to the council for this.
Any commercial property flooded due to the weather conditions or where a business could not function due to a lack of access is eligible for 100 per cent business rate relief for three months.
Any business that has not been contacted directly can apply for support at the council offices from the business support team.
For more information, contact Mark Shaw on 07973812510 or Elliot Payne on 07814051305.