Francois participated in the FCS team's first practice. He has two seasons of eligibility remaining.
"I am very happy that Deondre Francois is joining our program," second-year coach Robert Prunty said. "He is a cerebral football player with unbelievable athletic ability. More importantly, he is an outstanding young man who graduated Florida State in 3½ years. We are ecstatic to have Deondre Francois in our program."
Francois, 22, was dismissed from Florida State's program in February. A girlfriend posted on social media that he abused her, but Francois was not charged with a crime.
In April 2018, he was cited for misdemeanor possession of marijuana.
The 6-foot-2, 216-pound Francois was the Seminoles' starter in 2016 and last season, passing for 6,291 yards and 35 touchdowns in his career. He suffered a season-ending injury in the 2017 opener.
"It's a blessing to be here," Francois told the Daily Press of Newport News, Virginia. "Coming to a smaller school like this, it gives me a chance to focus.
"I was in the spotlight at Florida State, but coming to Hampton, it gives me the opportunity to be in a more family-oriented program. In a smaller atmosphere, I can focus on my schoolwork and stay out of trouble."
Hampton is returning mostly untested quarterbacks this season. The Pirates, in their first season in the Big South, will open the new campaign at home against Division II Elizabeth City State on Aug. 31.