Luetge, 34, had a 1.74 ERA in nine spring training appearances. A left-hander, he allowed his only runs on a pair of solo homers by Toronto's Teoscar Hernandez and Kevin Smith on March 21. He gave up eight hits in 10 1/3 innings with 18 strikeouts and two walks.
New York had an opening for a left-hander while Zack Britton recovers from surgery on March 15 to remove a bone chip in his pitching elbow and Justin Wilson builds arm strength after being sidelined during spring training by shoulder soreness.
"There was a lot of really good competition, frankly, better competition than I feel like we've had in the last several years," Yankees manager Aaron Boone said Wednesday.
"And there were a lot of different ways we we're considering going for that spot. But it's hard to deny what Lucas was able to come in really from the start of camp and really push his way onto the roster, earn his spot and excited to see what he can potentially go out and do for us."
Luetge pitched for Seattle from 2012-15, going 3-5 with a 4.35 ERA in 111 relief appearances with 74 strikeouts and 47 walks in 89 innings. He hasn't thrown more than nine innings in a major league season since 2013.
He became a free agent after the 2015 season and spent 2016 with Cincinnati and split 2017 in the Reds and Baltimore Orioles' organization. After not pitching in 2018, he spent 2019 in the Arizona Diamondbacks' organization and 2020 in the Oakland Athletics' organization.
In his previous major league appearance, Luetge pitched 2 1/3 hitless innings for the Mariners in an 8-5 home loss to Minnesota on April 25, 2015. He had pitched in 152 minor league regular-season games since then.
New York selected Luetge to the 40-man roster, placed Britton on the 60-day injured list, and placed first baseman Luke Voit (recovering from left knee surgery), infielder/outfielder Miguel Andújar (right wrist carpal tunnel syndrome) and Wilson (left shoulder inflammation) on the 10-day injured list, the 10-day moves retroactive to Monday.