The deal, which is pending a physical, also includes a third-year player option, a source confirmed to ESPN.
Right-handed Walker, 28, was 4-3 with a combined 2.70 ERA and 50 strikeouts in 53⅓ innings for the Seattle Mariners and Toronto Blue Jays in 2020. He has a five-pitch repertoire with a 93 mph fastball mixed among sliders, splitters, sinkers and curveballs.
Although Mets manager Luis Rojas cautioned that the deal was not yet final, he already was viewing the addition as a boost.
"A guy like him, it just makes your rotation so strong when you can add him," Rojas said Friday from spring training in Port St. Lucie, Florida.
New York's need for a pitcher increased with the loss of Seth Lugo, who will miss the start of the season after elbow surgery Tuesday to remove a bone spur. The team also hopes to get starter Noah Syndergaard back as soon as June. He is rehabbing from Tommy John surgery last March.
Walker has a career record of 35-34 with a 3.84 ERA in eight major league seasons. He made just one appearance in 2019 with the Arizona Diamondbacks after recovering from Tommy John surgery, which he had after making three starts in 2018.
"Looking at the history and his season last year, everything that he can bring to a team is pretty outstanding," Rojas said. "You talk about talent plus experience. Around the league, players that have been in the same clubhouse as him, we heard about some leadership."
Walker's deal with the Mets was first reported by SNY.
The Associated Press contributed to this report.