The other two prospects going to Seattle are outfielder Dom Thompson-Williams and right-handed pitcher Erik Swanson.
Paxton, who turned 30 this month, has spent his entire career with Seattle. He went 11-6 in 28 starts last season with a 3.76 ERA, and his 208 strikeouts ranked ninth in the American League. He threw a no-hitter against the Blue Jays on May 8.
"I couldn't be more excited about it," Paxton said Monday. "It's going to be a fantastic opportunity in New York, always expecting to win, the way I do. I'm looking forward to being a part of a fantastic team."
The move bolsters the Yankees' thin starting rotation, which contributed to New York's loss in the AL Division Series to the eventual World Series champion Red Sox. He joins a rotation projected to include right-handers Luis Severino and Masahiro Tanaka and left-hander CC Sabathia.
General manager Brian Cashman wants to add at least one more starter, address the shortstop opening created by Didi Gregorius' elbow surgery and add to his bullpen. He is aggressively pursuing pitching from outside the organization, even after Sonny Gray, who was acquired by the Yankees before the 2017 trade deadline, flamed out with New York, shaken by repeated booing at Yankee Stadium.
"I can't tell you we've learned anything further other than we drill down as much as we can, whether with players that have played with somebody as teammates that we know or coaches who have coached or people who have managed or anybody, whether it's all the way back in the amateur ranks," Cashman said. "We just try to ask a lot of questions about how they compete. This environment can bring out a different experience for some. So I don't have a new secret formula to address predictability on who will thrive and survive and who won't here in New York."
Paxton made $4.9 million last season and is eligible for salary arbitration. He can become a free agent after the 2020 season.
"I think I'll be a great fit. They seem very committed to winning, and so am I," Paxton said.
Paxton is 41-26 in six major league seasons, making six trips to the disabled list in the past five years. He missed nearly four months with a strained left latissimus dorsi muscle in 2014, 3½ months with a strained tendon in his left middle finger in 2015, 10 days with a bruised left elbow in 2016, 3½ weeks with a strained left forearm and a month with a strained left pectoral muscle in 2017, and 2½ weeks with lower back inflammation this year.
"I continue to try to work towards being healthy for an entire season," he said. "All the injuries that I've had haven't reoccurred. I've learned how to make sure those things don't happen again through exercise or whatever."
When he went to Triple-A two years ago, he worked with former big league pitcher Lance Painter, who told him to drop his arm angle back to three-quarters. When Paxton returned to the Mariners, he studied reading swings with pitching coach Mel Stottlemyre Jr.
"It's taken me a little longer, I think, in my career because I have had so much time off," Paxton said. "But having those larger chunks the last couple years has really allowed me to come into my own and really make some big strides, and I look forward to continuing to make big strides in my game. And I think that my best baseball is still to come.''
A proud Canadian born in a fishing village in the suburbs of Vancouver, British Columbia, Paxton is also known for keeping his composure, as a bald eagle mistakenly landed on his shoulder before a start at Minnesota in April.
Meanwhile, Seattle decided to rebuild after going 89-73 and finishing third in the AL West, 14 games behind division-winning Houston and six back of Oakland.
"Clearly we've opted 2019 be a year that we take a step back hoping to take two forward," general manager Jerry Dipoto said. "When I say 2020 and 2021, it's simply gauging the ages of the players we're building around here."
Sheffield, a first-round pick of the Indians in 2014, is the Yankees' No. 1 prospect and made his major league debut in September with three relief appearances.
The 22-year-old was No. 12 on Keith Law's 2018 midseason rankings of all prospects in baseball. He went 7-6 with a 2.48 ERA in 25 games (20 starts) with Double-A Trenton and Triple-A Scranton/Wilkes-Barre this year.
@Yankees thank you to all the fans who followed me to my path to the Bronx! It's been an amazing journey so, but we just now beginning! To my teammates and coaches nothing but best of luck and thank you for everything! So with that being said......— Justus Sheffield (@Topsheff42) November 20, 2018
Sheffield had just finished playing golf when he saw Cashman's number on his cellphone.
"Definitely caught me by surprise," Sheffield said.
Swanson, the Yankees' No. 22 prospect, according to MLB.com, was promoted to Triple-A last season, where he went 3-2 with a 3.98 ERA in 13 starts with 78 strikeouts and 14 walks.
"I think both of them are going to compete for a spot in the rotation," Dipoto said of Sheffield and Swanson. "We absolutely expect to see both guys before the summer is through in Seattle, and they will start cutting their teeth here and hopefully set us up for what we think will be a pretty exciting group as we enter 2020 and 2021.''
The Yankees picked Thompson-Williams in the fifth round in 2016. The 23-year-old hit .299 with 22 home runs and 20 stolen bases in Class A with Tampa and Charleston this year.
Information from The Associated Press was used in this report.