Rodriguez was taken from the Rays with the eighth pick in the first round, and Pendleton was selected from the Yankees in the second round, with the 17th overall pick.
Astros general manager Ed Wade said both will come to Spring Training bidding to crack the rotation. The Astros didn't lose any players in the Major League portion of the Draft.
"We're excited to get the two guys," Wade said. "We had three names on our list, and we got two of the three guys we wanted."
The other name on the Astros' wish list was right-hander Elvin Ramirez, who was taken by the Nationals from the Mets. Wade said he tried to trade up to take Ramirez, but nothing materialized.
"Being able to get these two guys provides us with depth of competition for a starting role in Spring Training, and we'll see where it goes from there," Wade said. "It's good to add some quality in the organization, and we understand what the Rule 5 process is and are satisfied with the way it went."
Houston lost right-hander Jeiler Castillo to the A's in the Triple-A phase of the Draft, but Wade didn't consider the loss to be very consequential.
During the Major League phase of the Rule 5 Draft, players left unprotected may be selected for $50,000. The selection rules provide that a player must remain on the drafting team's active Major League roster during the following season or be offered back to the original club at half the original price.
Rodriguez, 22, went a combined 7-5 with a 3.71 ERA in 29 games (19 starts) between Triple-A Durham and Double-A Montgomery of the Rays organization last season. He spent most of the year at Durham, going 6-5 with a 3.80 ERA. He's currently pitching in the Dominican Winter League.
He throws between 88-92 mph with his fastball and had glowing reports from director of Latin American scouting Felix Francisco.
"He's a guy who knows how to pitch," Wade said. "He's not just a hard thrower. He's still young, and hopefully we can get both these guys in front of [pitching coach] Brad Arnsberg and the staff at Spring Training and they can get the most out of them and give them a chance to make the club."
Pendleton, 27, went a combined 12-5 with a 3.61 ERA in 29 games (27 starts) last season in the Yankees organization. He spent most of the year with Double-A Trenton, going 10-4, and appeared in five games at Triple-A Scranton/Wilkes-Barre.
A native of the Houston area and product of Rice University, he has a 89-93 mph fastball and has overcome some elbow problems.
"We just think with his control and his command, he's got a chance to come in and compete, and that's all we can ask him to do at this point in time - take advantage of the opportunity to be at big league camp and see where it takes him," Wade said.
Brian McTaggart is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.