The 24-year-old signs a two-year deal at the Stadium of Light, after making almost 200 appearances for the Gills.
"It feels very nice to be here and means a lot," he said. "I am quite calm at the moment - it has not sunk in yet that I am a Premier League player," beamed Nosworthy.
"When I am introduced to the rest of the lads next month, it will be different, but I am looking forward to it."
Sunderland boss Mick McCarthy said: "We are delighted to have signed Nyron, who joins the club as an experienced defender despite his relatively young age.
"I am sure he will provide Stephen Wright with strong competition for the right-back berth next season.''