Norris becomes the highest-paid player on the club, as it moves to the American League in 2013, by agreeing to a $3 million deal, which is nearly six times higher than his 2012 salary. Lowrie more than doubled his salary, agreeing to sign for $2.4 million. Terms of the Wright deal weren't known.
The Astros reached agreements with all three players before Friday's noon CT deadline to exchange numbers.
"I think the salary arbitration process is designed to promote settlements and promote communications between the clubs and agents to reach a value both parties deem appropriate," Astros assistant general manager David Stearns said. "We're happy to be able to do that with all three of our players prior to exchanging filing numbers. Sometimes you have to go deeper into the process, but we were able to come to an agreement both sides found worthwhile."
Norris, 27, was 7-13 with a 4.65 ERA in 29 starts last year, allowing 165 hits and striking out 165 in 168 1/3 innings. He had hoped to sign for $3 million based on comparable players, and he will be the highest-paid player on Houston's roster this year, eclipsing Carlos Pena's $2.9 million base salary.
"I'm excited," Norris said. "I'm happy the Astros stepped up to the plate. I'm happy to have this done and behind me and can focus on playing baseball."
The 28-year-old Lowrie, who made $1.15 million last year, set career highs in games (97), at-bats (340), runs (43), hits (83), home runs (16) and walks (43) despite missing 52 games with a sprained right ankle and leg injury. He wound up hitting .244 with 42 RBIs.
"I'm really happy about it," Lowrie said. "I think we came to a fair deal, and I'm just excited to get out there and get on the field and put in some good work this year and help the Astros' organization get to where they wanted to be."
Lowrie has one more year of arbitration before he becomes a free agent, and he would like to remain in Houston for the long haul, though he hasn't been approached by the team about any kind of multiyear deal.
"I'm certainly open to it," Lowrie said. "That's something every player looks forward to, and I'm no different. As the organization continues to improve and they continue to invest, I think the team will continue to get better, and hopefully I can be a part of that. I enjoyed my first year in Houston, and hopefully I can stay around for a few more."
Wright, 27, was 2-2 with a 3.27 ERA in a career-high 77 games last year, which led the Astros and ranked tied for sixth in the National League. His .226 batting average allowed ranked fifth in the NL among left-handed relievers.
"I'm happy to have it behind me and can focus on the upcoming season and going out and doing my best to help us win some ballgames," Wright said. "It's good to know that part of the situation is taken care of and we can focus on baseball activities."