It comes after the water firm contacted the Phone-Paid Service Authority (PSA), after receiving a complaint from a customer.
The PSA upheld YW's complaint after finding websites quoting premium-rate numbers for customers to call the company.
The official number is a local rate 0345 number, but some customers were unwittingly using the call connection service and being charged Â£6 per connection.
The PSA cited four breaches relating to call connection services operating on the number range 0901 545* and 09011 506*.
A statement from the PSA to Yorkshire Water read: “The provider has agreed to provide refunds to consumers who make a valid claim.
"Should you wish to discuss a refund you will need to contact the provider directly.”
It said customers may be asked to provide a copy of a phone bill highlighting the relevant premium rate charges before a refund is issued.
A spokesperson from Yorkshire Water said: “We are pleased with this outcome.
"We have lots of free ways that our customers can contact us via our website. They can use live chat, request a free call back with a precise 10 minute slot that suits them, or they can talk to us via Twitter and Facebook.
"If they do need to phone us, we have a local rate 0345 number to use.
“We object to these call connection service charges for a simple phone call to us which can be made direct to us and charged at a local rate."
In April 2017, the PSA issued a Â£645,000 fine to a similar call connection company called DK Call which charged customers Â£3.60 per minute to call well-known organisations such as Sky and HMRC.