The Dragons made the announcement on Tuesday and will now undertake a search for a replacement, with Webb to depart in April.
The call looms as crucial as the Dragons look to build on improvements made during Shane Flanagan's first season at the helm, which ended just short of a first finals berth since 2018.
Webb helped the Dragons navigate the tumultuous Covid-19 period after taking charge in April 2020, the club's infamous biosecurity barbecue breach at the house of player Paul Vaughan proving a high-profile challenge for the club.
Under Webb's leadership, the club talked captain Ben Hunt down from his release request following the axing of coach Anthony Griffin, though the halfback's future will once again be in the spotlight given his contract is due to expire next year.
Webb also helped oversee the hiring of coach Flanagan, and the recruitment of incoming players Valentine Holmes and Damien Cook.
"Ryan is a great person and has been a strong leader for club," chairman Andrew Lancaster said.
"He took on the role during a testing time as COVID impacted the NRL, bringing in much-needed reforms and guiding us through a period of significant change over recent years.
"Ryan's efforts have set us up for continued growth.
"He has worked closely with the Board, players, staff and fans to ensure that the Dragons will continue building into the future."
Webb had previously served as Wests Tigers' chief operating officer for three-and-a-half years and as a marketing and commercial manager at AFL Victoria prior to that.
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