He is listed as the No. 5 defensive tackle in the position rankings by ESPN's Mel Kiper Jr.
"This past year has been crazy for so many people," Twyman said in his post on Twitter. "It makes you realize you have responsibilities beyond yourself. That's why I have decided to opt out of the 2020 season and declare for the 2021 NFL draft, and to return home to be with my family.
"This isn't about COVID-19. This is about my family's needs, now and in the future."
Twyman had 10.5 sacks and 41 tackles en route to becoming an All-ACC first-team selection and a second-team All-American as a sophomore last season.
He thanked Pitt coach Pat Narduzzi, coaches and fans, and he said he plans on returning to the university in the future to complete his degree in communications.
"I want to thank Panther Nation for their love," Twyman said. "I will miss running out of that Heinz Field tunnel and hearing 'Thunderstruck.'"
Twyman was thrust into a starting role last summer following an injury to Rashad Weaver during training camp. He wasted little time making an impression, collecting three sacks in a win over Ohio in Week 2, the highest single-game sack total for a Pitt defensive lineman since current Los Angeles Rams star Aaron Donald did it in 2011.
Twyman's departure deals a blow to a defensive line that figures to be one of the best in the Atlantic Coast Conference and perhaps the nation.
The Associated Press contributed to this report.