Financial terms were not released.
"I am very excited to be a Senator," Tkachuk told NHL.com. "It was a tough choice because I loved my time at Boston University. I want to thank everyone who has helped me. I'm super excited to get things started."
The 18-year-old forward was selected by the Senators with the No. 4 pick in the 2018 NHL Draft. He had 31 points (eight goals, 23 assists) in 40 games last season, and led Boston University in assists and shots on goal (131). He also helped the United States win the bronze medal at the 2018 IIHF World Junior Championship with nine points (three goals, six assists) in seven games.
Tkachuk (6-foot-3, 196 pounds) chose to sign his first professional contract rather than return to college for his sophomore season. He is eligible to play for Belleville in the American Hockey League because he was drafted from an NCAA team.
"Brady Tkachuk exemplifies all the attributes around which we want to improve the Ottawa Senators," general manager Pierre Dorion said. "He is a young man of exceptional character. We know how much he agonized over leaving Boston University, and we are encouraged by the degree of accountability and commitment this shows from him.
"Through tenacity, combativeness and work ethic, he also exemplifies leadership skills that we know will benefit the team now and well into the future. Most of all, Brady has shown us through his maturity that he is coachable, committed to teamwork and determined to help us strengthen our team chemistry. For all these reasons, he is an exciting young player whose growth and development we are eager to support."
Tkachuk's father, United States Hockey Hall of Fame member Keith Tkachuk, told NHL.com on Saturday that Brady opted to turn pro.
"We had Brady home this weekend and he decided to sign," Keith Tkachuk said. "He is so emotional right now because he loves [Boston University] and his teammates."
While skating with the U.S. at the World Junior Summer Showcase in Kamloops, British Columbia from July 28-Aug. 4, Tkachuk said his choice would be made after returning home to St. Louis and speaking with his family, including his father and older brother, Calgary Flames forward Matthew Tkachuk.
"The decision will be based on what's best for my development short- and long-term," he said. "I want to have a long career and don't want to go somewhere and not have an impact. I want to make an impact wherever I go and be able to contribute and play my best."
NHL.com staff writer Mike G. Morreale contributed to this report.
