The 49ers have waived offensive lineman Alan Knott to make room on the roster.
Morris joined his new teammates in Houston on Tuesday and will get to work during two joint practices with the Texans this week. The 49ers are down two running backs. Neither Jerick McKinnon nor his backup, Matt Breida, will practice this week or play in Saturday's exhibition matchup at NRG Stadium against the Texans.
The 49ers have also been without running back Joe Williams, who was on the East Coast to attend the funeral services for his brother-in-law. Williams, like Morris, will join his teammates in Texas on Tuesday.
Shanahan believes Morris, whom he coached in Washington while he was the offensive coordinator there, will be able to step in right away. The running back is already familiar with his system.
"There's not big changes, and it's not that tough for a back," Shanahan said on Monday. "They've got to set their track the right way, and you hand it off to them, and go run.
"We have a way that we coach guys and stuff, but everyone, when you're away from something, it's going to take some time. He is going to be rusty with that stuff, but he'll get the hang of it, get his tracks consistent and run hard."
The Washington Redskins made Morris a sixth-round draft pick in 2012. He spent the last two seasons with the Cowboys and served as the starting running back in 2017 while Ezekiel Elliott served a six-game suspension. The two-time Pro Bowl selection (2013, 2014) has registered 5,503 rushing yards on 1,262 carries with 32 touchdowns in six NFL seasons while adding 57 receptions for 421 yards.
"It's not flashy, but he runs extremely hard," Shanahan said of Morris. "He's very reliable. You're blocking for zero, usually, he can get at least one. He's a hard-nosed runner who you can keep handing the ball off to."
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