The Herefordshire-based firm won the right to build the structures on appeal after Swale Borough Council refused its original planning application. The 18ha of polytunnels will be built at S&A Hernhill Nurseries near Faversham, Kent.
Some local residents opposed the scheme but S&A said it would create jobs and reduce the amount of fruit being imported into the UK.
Jason Davies-Baker, site director at Hernhill Nurseries, said: "We are delighted with this decision - we have worked hard on our proposals for this site and we can now move forward and put our plans into action."
He added: "While we recognise that there has been some local opposition to this decision, we believe this development is an important one, not only for our business but also for the local economy.
"There is a very high demand for British strawberries in the UK and a real need for additional capacity in polytunnels in order to keep up with this demand. By installing polytunnels at our site we can continue to provide local produce to a demanding market.
"We will also be able to provide dozens of new jobs for local people, and significantly increase the economic benefit we bring to the local economy each year.
"We will also be developing and operating the site with the views of local people in mind. We will be putting plans in place for landscaping and screening around the site boundary in order to minimise visual impact on those living nearby, and agreeing a site management plan to minimise any impact our operation will have locally."