The World number 161, who at this year's Roland Garros became the oldest Grand Slam debutant since 43-year-old Renee Richards at the 1977 U.S. Open, meets a player six years her senior and pushing for a record-equalling 24th major title.
"It's a dream come true," Gatto-Monticone said after coming through the qualifying rounds at Wimbledon to set up a meeting with the seven-times winner.
Williams is chasing her own dream of equalling Margaret Court's all-time Slam record and has been stuck on 23 major titles for over two years, with poor form putting a question mark over her chances of achieving the feat at Wimbledon.
The American has not enjoyed the best preparation for the tournament, with a niggling knee injury limiting her time on court since the Australian Open in January, but Williams will expect to see off Gatto-Monticone in their first meeting.
"Obviously, I haven't had the best time and preparation that I normally would have," 11th-seeded Williams said.
"I've had a good week-and-a-half, but I have been really just mentally training, physically training for that time here. I'm just going to do the best that I can now that I'm here."
Holder Angelique Kerber begins proceedings on Centre Court against German counterpart Tatjana Maria.
Roger Federer, fresh from his 10th title at Halle, launches his quest for a ninth Wimbledon crown against Lloyd Harris of South Africa while Rafa Nadal meets Japan's Yuichi Sugita.
French Open winner and Wimbledon top seed Ash Barty of Australia takes on China's Zheng Saisai.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Ken Ferris)
