Ellsbury is the second major free-agent addition in the Yankees' offseason rebuilding. He was to take a physical in New York on Wednesday, the person said, speaking on condition of anonymity because no statements were authorized.
The Yankees also had been negotiating with Shin-Soo Choo, who like Ellsbury is represented by agent Scott Boras.
Earlier Tuesday, New York finalized an $85 million, five-year contract with All-Star catcher Brian McCann.
There is a long history of stars moving from Beantown to the Big Apple during their careers. Babe Ruth was the most famous, and Roger Clemens, Wade Boggs and Johnny Damon followed.
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 RBIs.
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 $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.
New York also has been speaking with the agents for Robinson Cano, their All-Star second baseman. The Yankees, who rebuffed his request for a 10-year deal worth more than $300 million, believe he has been in talks with the Seattle Mariners.
Ellsbury won a pair of World Series titles with the Red Sox and was an All-Star in 2011.
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 RBIs 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 RBIs.
Following the departure of Russell Martin last offseason, Yankees catchers combined for a .213 average, eight homers and 43 RBIs, 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."
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