The terms of the deal, which is pending a physical, were first reported by Mark Feinsand of the New York Daily News.
It's the third-richest contract for an outfielder in MLB history, following Manny Ramirez's $160 million deal with the Red Sox and Matt Kemp's $160 million deal with the Dodgers.
Ellsbury's deal includes a $21 million option for the 2021 season, with a $5 million buyout. If the option is exercised, the deal would be worth $169 million over eight years.
The move would raise the Yankees' luxury tax payroll to about $138 million for 10 players. The Yankees hope to get under the $189 million tax threshold next season, which includes about $177 million for salaries for the 40-man roster and approximately $12 million for benefits.
Ellsbury, who turned 30 in September, led the majors with 52 stolen bases despite being hobbled late in the season by a broken right foot. The lefty-hitting leadoff man batted .298 with nine homers and 53 RBI, and the short right-field porch at Yankee Stadium should boost his power numbers.
Ellsbury, who missed half of the 2012 season due to injury, just completed his seventh season in the majors, all with the Red Sox. He won a pair of World Series titles with the Red Sox and was an All-Star in 2011, when he finished second to Detroit's Justin Verlander in AL MVP voting. He has reached the postseason four times and is a career .301 hitter in those 38 games.
Ellsbury played a huge role in Boston's World Series run in the postseason, hitting .500 (9 for 18) in the ALDS vs. Tampa Bay, .318 (7 for 22) in the ALCS vs. Detroit, and .240 (6 for 25) vs. St. Louis in the World Series. He led the postseason with 14 runs and six stolen bases, which is the same style of play he brings to the ballpark every day and why the Yankees are willing to pay such a big contract.
The Oregon State product was one of the top two free agents on the market -- the other being Yankees second baseman Robinson Cano.
Ellsbury is the second major free-agent addition in the Yankees' offseason rebuilding after they missed the playoffs for just the second time in 19 years. Earlier Tuesday, New York finalized an $85 million, five-year contract with All-Star catcher Brian McCann.
The Yankees also had been negotiating with outfielder Shin-Soo Choo, who like Ellsbury is represented by agent Scott Boras.
After their playoff absence, the Yankees are undergoing a major transformation. Closer Mariano Rivera and Andy Pettitte are retiring, Phil Hughes is leaving to sign with Minnesota and New York appears to be making little effort to retain outfielder Curtis Granderson.
McCann, a seven-time All-Star, is to be introduced at a news conference Thursday at Yankee Stadium.
He receives $17 million in each of the next five seasons, and the Yankees have a $15 million option for 2019 with no buyout. The option becomes McCann's if he has at least 1,000 plate appearances combined in 2017 and 2018, has at least 90 starts at catcher in 2018 and does not end the 2018 season on the disabled list.
His deal includes a full no-trade provision, meaning he cannot be dealt without his consent.
McCann, who turns 30 in February, hit .256 with 20 homers and 57 RBI in 102 games this year, when he missed the first month following offseason surgery on his right shoulder. He has a .277 average in nine big league seasons with 176 homers and 661 RBI.
Following the departure of Russell Martin last offseason, Yankees catchers combined for a .213 average, eight homers and 43 RBI, according to STATS, down from .220, 22 and 64 in 2012.
''We feel we have made a significant improvement to a key position, while adding a high-character presence to our clubhouse,'' Yankees managing general partner Hal Steinbrenner said in a statement. ''Our work this offseason has just begun, but we feel this is an important step towards what will be an exciting and rewarding 2014 season for our fans.''
The Red Sox made a $14.1 million qualifying offer to Ellsbury along with Mike Napoli and Stephen Drew, both of whom are still free agents. Boston went from worst to first a year after dumping three of their biggest contracts -- Josh Beckett, Adrian Gonzalez and Carl Crawford -- on the Los Angeles Dodgers at a savings of about $261.7 million. Instead of making a big splash in free agency last offseason, they signed mid-market players like Napoli, Drew, Shane Victorino, Jonny Gomes and Koji Uehara.
GM Ben Cherington said the lessons learned from their successes and failures won't be forgotten.
''We have to go into this offseason with the same general mindset: to build a roster as deep as we can,'' he said last month. ''The general philosophy would lead us toward a lot of the same things we were looking for last year.''
''Jacoby's a terrific player, as everyone knows. Of course we know we're a better team when he's on the field than when he's not,'' Cherington said, adding that if they could not sign him they would consider moving Victorino, who won a Gold Glove in left field, to center field and looking for a corner outfielder.
Cherington also let catcher Jarrod Saltalamacchia go, replacing him with A.J. Pierzynski on a one-year, $8.25 million deal.
The Red Sox have a surplus of veteran pitchers with Jon Lester, John Lackey, Clay Buchholz, Jake Peavy, Felix Doubront and Ryan Dempster all signed. Some of those could be gone since the Red Sox have youngsters, including rookie Brandon Workman, who might be ready for the rotation.
But the veterans did their part in getting the Red Sox to the World Series, where Lester went 2-0 and Lackey won the deciding Game 6.
Ellsbury is just the latest Sox star to switch sides in the rivalry with the Yanks. Johnny Damon made the same move in 2006, two years after helping snap the Sox's Series drought, signing with New York for four years and $52 million. He followed Roger Clemens, Wade Boggs and Babe Ruth.