The Texans have wrapped up their draft class, getting the final choice under contract Tuesday afternoon.
Coulter was the final of five draft picks the Texans made in April. They used the 171st overall selection on him.
Last season as a junior at Rhode Island, Coulter made 72 catches for 1,039 yards and eight touchdowns. He was the seventh Rams player to have a 1,000-yard receiving season.
Coulter earned second-team all-Colonial Athletic Association honors in 2019.