Albers, who attended Clements High School in the Houston suburb of Sugar Land, appeared in 56 games last season for Cleveland and was 3-1 with a 3.14 ERA. He's pitched eight years in the Majors, including his first two with Houston (2006-07) and three with Baltimore (2008-10).
The deal is worth a reported $2.45 million in 2014 with a $3 million option for 2015.
"It's really a good fit to be able to come in and try to do just what I've been doing the last few years, and hopefully help get this team back on track," Albers told MLB.com. "As soon as I knew Houston was really involved, I knew this is where I wanted to be. I was real excited when they made me a good offer, and I was ready to accept it."
The addition of Qualls and Albers shores up an Astros bullpen that led the league in blown saves last season and went with a closing contingent of young arms. Luhnow didn't rule out signing another reliever.
All three pitchers the Astros have signed this month, including starter Scott Feldman, are strike-throwers who have high ground-ball rates. Albers' ground-ball percentage of 81.3 percent was tops among all AL pitchers in 2013 (min. 50 appearances).
"There is a thread among the pitchers we acquired," Luhnow said. "They all throw strikes and they keep the ball on the ground, and I think that's going to do well in our ballpark. Obviously, the last couple of guys are former Astros, and it's always nice when guys we drafted and got to the big leagues with us come back later in their career."
Since he was traded following the 2007 season, Albers spent three years in Baltimore, 1 1/2 years in Boston, half a season in Arizona and spent last season with the Indians. He has a career 25-31 record with a 4.49 ERA in 356 career appearances.
"I've been around to a few teams, but being back here is nice," Albers said. "Last year, I was kind of a middle reliever, and years before that, more of a back-end guy. Hopefully, this year coming in I can compete for a back-end spot. That would be nice."
Albers was sent to Baltimore along with Mike Costanzo, Troy Patton, Dennis Sarfate and Luke Scott in a blockbuster deal on Dec. 12, 2007, in exchange for Miguel Tejada. Qualls was traded away from Houston two days later when he was sent to Arizona along with Chris Burke and Juan Gutierrez for closer Jose Valverde.
Albers says he's matured since his first stint in Houston, when he was called up as a starter for a team that was coming off a World Series appearance. The Astros still believed they could contend, which is why they shipped Albers and other prospects to Baltimore to acquire Tejada.
"That was quite a while ago," Albers said. "I've gotten older, matured and gotten married. I just really continued going forward. It might have been good for me to get traded to Baltimore and be able to go there and Boston and Arizona and Cleveland. Just to be able to come home is real exciting."