Greenard is the second of the Texans' five 2020 draft picks to agree to terms.
At 6'3", 263 pounds, Greenard is expected to contribute to the Texans' pass rush, which ranked toward the bottom of the league in 2019.
As a graduate transfer at Florida last season, Greenard led the SEC with 9.5 sacks and 15.5 tackles for loss.