Hurley said he told his team earlier Tuesday that he was leaving for the Rams.
Multiple media reports said Hurley's deal is for six years.
Hurley is replacing Jim Baron, who coached the Rams since 2001 but wasn't able to get them into the NCAA tournament. Baron finished a disappointing 7-24 this season, 4-12 in the Atlantic-10, and was fired March 4.
Hurley and his wife toured the Kingston campus earlier in the week. During the weekend, Hurley told ESPN.com, he had to think about what he was going to do, and said that reports that he had already accepted the job were premature.
Rhode Island has scheduled a 1 p.m. ET Wednesday news conference.
Hurley coached Wagner for two seasons, going 38-23 overall and 25-6 this season. Wagner lost to Robert Morris in the NEC tournament semifinals; the highlight of the season was when Wagner won at Pitt.
Hurley was a successful high school coach at St. Benedict's in New Jersey.
A key member of the former staff is Preston Murphy, who has recruited well for Rhode Island. Murphy, a former Ram, is beloved at URI and his presence would be vital in getting some of the top recruits to stay. Rhode Island athletic director Thorr Bjorn conveyed to all candidates for the job that keeping Murphy would be a good idea.