The company acknowledged that residents near Saltend wastewater treatment works had put up with unacceptable stink on and off since 2000.
However, a local councillor said the cash sum was “shameful” and only amounted to around £1 per person.
Richard Sears, community engagement manager, said: “We want to be a good neighbour and this trust fund underlines our commitment to working alongside the local community and doing what we can to give something back through this £50,000 cash fund.”
The company has set up a 10 person panel of councillors, residents and local business representatives to assess bids for the community fund.
Panel member and councillor Mike Bryan said: “The people living and working around Hull sewage works have patiently put up with odours for a long time.
He added: “I think we should welcome this generosity and I do hope this will be of real benefit to our community.”
However, East Ridings councillor John Dennis told the BBC he had proposed a fund twice the size.
He said: “Local residents have endured enormous discomfort and inconvenience over the past 12 years, ever since the Saltend wastewater plant first opened, and for Yorkshire Water to come up with a figure that equates to only around £1 per person is, frankly, shameful.”
Yorkshire Water installed a £3.5 million odour control unit in December 2011 that it said had significantly reduced the smell, leading to a drop in complaints.