In its business plan submitted to Ofwat, the water company said it will keep bill charges below inflation for the next six years.
So far Anglian, Southern, Northumbrian and Severn Trent Water have proposed similar measures.
Thames Water is the only company to have announced a price rise.
Wessex said its submission to Ofwat followed the company’s “biggest and most in-depth” customer consultation exercise which involved getting views of more than 21,000 customers and 90 stakeholders.
It is also proposing to invest around £1.2 billion between 2015 and 2020 to improve water and sewerage infrastructure.
The company said bills will fall in real terms from next year, with the average household bill in 2019-20 being £454 compared to the current average bill of £479 a year.
Colin Skellett, chairman of Wessex Water, said: “We plan to keep bill charges to below inflation for the next six years, so bills will go down in real terms, while at the same time we will continue investing in high standards of service for customers and the environment.
“This investment will improve the resilience of our services – halving the number of properties fed from one water supply source and solving flooding issues, as well as reducing leakage further and fixing leaks quicker. Wherever possible we will use innovative approaches to make improvements in cheaper and more efficient ways, which will benefit customers in the long term.”