The move means the Yankees won't receive draft pick compensation if Gregorius signs elsewhere. New York still could try to re-sign him.
Gregorius, 29, was arguably one of the Yankees' best players before undergoing Tommy John surgery that limited him to 82 games last season.
From 2016 to '18, Gregorius averaged over 20 home runs per season. He drove in a career-high 87 runs in 2017 and 86 the next year. In last season's abbreviated campaign he still hit 16 homers and drove in 61 runs.
Gregorius has never been a big on-base player, but he has made up for that with power and solid defense.
Other big names did receive qualifying offers on Monday. Those getting it were Jose Abreu (White Sox), Madison Bumgarner (Giants), Gerrit Cole (Astros), Josh Donaldson (Braves), Jake Odorizzi (Twins), Marcell Ozuna (Cardinals), Anthony Rendon (Nationals), Will Smith (Giants), Stephen Strasburg (Nationals), and Zack Wheeler (Mets).
In other Yankees moves, Tyler Lyons, who earned a spot on the Yankees' postseason roster as a left-handed reliever, refused an outright assignment to Triple-A Scranton/Wilkes-Barre and elected to become a free agent.
The 31-year-old was released by Pittsburgh in August and signed with New York. He struck out 12 and walked two in 8 2/3 innings during 11 appearances with the Yankees in September. He made one appearance each in the division series against Minnesota and the championship series against Houston, striking out four over 1 2/3 hitless innings.
New York reinstated third baseman Miguel Andujar, first baseman Greg Bird, right-handers Jonathan Holder and Jake Barrett, and outfielder Jacoby Ellsbury from the 60-day injured list on Monday and assigned Barrett outright to Scranton/Wilkes-Barre.
Ellsbury has not played since 2017 because of a variety of ailments. He is owed $21,142,857 next year in the final guaranteed season of a $153 million, seven-year contract, which includes a $5 million buyout of a $21 million option for 2021.
Information from The Associated Press was used in this report.