Foster's release was listed with a failed physical designation on the NFL's transaction wire. He played just four games last season after suffering injuries to his groin and Achilles tendon.
"There are not many players I respect more than Arian Foster," Texans general manager Rick Smith said in a statement. "He maximized his opportunity as an undrafted college free agent and worked to become the most productive back in franchise history, and one of the most complete backs in the NFL during his tenure with the Texans.
"Arian has contributed much, and meant a great deal to the success of the franchise over the past seven seasons and we wish only the best as he continues his playing career."
Foster, who rushed for a total of 6,472 yards and 54 touchdowns with the Texans, both franchise highs, was due a $6.5 million base salary with a salary-cap number of almost $9 million for the 2016 season. By releasing him, the Texans save around $6.6 million, according to ESPN Stats & Information.
Releasing Moore saves the Texans about $2 million in cap space, while parting ways with Graham saves the team a little more than $3.8 million under the cap.
Last week, Smith said the decision to release Foster would not be based on his salary. The Texans did not offer Foster a pay cut before releasing him. They simply couldn't count on his availability anymore, as he approaches his 30th birthday in August.
The last time Foster played in all 16 games was in 2012. During the 2015 season, he missed 12 games due to a groin injury he suffered during the Texans' first padded training camp practice in August and a torn Achilles tendon in Week 7. He had his second surgery of the season after the tendon tear and missed the rest of the year. He posted career-worst totals in yards per rush, rushing yards per game and first-down percentage while the Texans averaged 3.67 yards per carry in 2015, ranking 28th in the league.
Foster has a long history of injuries in his career, a trend that was likely made worse by the unusually high number of carries Foster took during his seven seasons with the Texans.
Since becoming Houston's starting running back in 2010, Foster leads the NFL in carries per game. He has suffered a torn meniscus, multiple hamstring injuries, a knee injury, a back injury that required surgery, a minor groin injury, a major groin injury and a torn Achilles tendon.
Foster came to the Texans as an undrafted free agent in 2009. He spent most of that season on the team's practice squad, then was elevated to the active roster in November.
The 2010 season marked his breakout year. Foster rushed 33 times for 231 yards in a season-opening win over the Indianapolis Colts, sealing his role as the Texans' starting running back. Foster won the rushing title that year, gaining 1,616 yards on 327 carries, and went to the first of his four Pro Bowls.
A hamstring injury hampered Foster at the start of 2011, and he missed two games. He rushed 278 times for 1,224 yards that season, gaining another 285 in the first two playoff games in franchise history.
Foster stayed healthy in 2012, but soft-tissue injuries returned in 2013, hampering him in training camp. Then Foster suffered a season-ending back injury that caused him to miss eight games. The Texans went 2-14, and the coaching staff was fired after the season.
The new coaching staff relied heavily on Foster at first. Foster had 55 carries in his first two games under coach Bill O'Brien -- one of the highest two-game totals in the past 10 years in the NFL.
Foster suffered a hamstring injury in the next game and missed one game and part of the next with the injury. He was on the injury report with a knee injury later that season and missed two games in November with a groin injury.
By that point, the Texans had resigned themselves to the fact that one of the most dynamic running backs in the league was going to occasionally miss games.
It seems that after last season, the risk finally became greater than the reward, and Foster no longer fit the Texans' plans.
The Texans signed Moore to a three-year deal worth $12 million last March after he spent the first four years of his career with the Denver Broncos.
Moore became the Texans' starting safety but was benched after Week 7. Not only did the Texans take him out of the starting lineup, they made him inactive for the rest of the season.
ESPN staff writer Tania Ganguli and ESPN Stats & Information contributed to this report.