The team also completed its deal with Mark Canha, another free agent outfielder. Canha gets $26.5 million over two years with a club option for 2024.
The 33-year-old Marte played for Miami and Oakland this year, batting .310 with 12 homers, 55 RBI and a major league-high 47 steals in 120 games.
The speedy center fielder will earn a $14.5 million salary next season and $19.5 million each of the following three years. He gets a $5 million signing bonus, payable in $2.5 million installments on Jan. 31 each of the next two years.
"Starling is a premier talent at a premier position," new Mets general manager Billy Eppler said in a statement. "His play in the outfield makes the team stronger at run prevention up the middle and his elite baserunning skills are a perfect blend. He has a winning attitude and will be a huge asset as well in our clubhouse."
The 32-year-old Canha, who can also play first base, hit .231 with 17 homers, 61 RBI and 12 steals in 141 games with Oakland this year. He spent his first seven big league seasons with the Athletics, batting .244 with 89 homers and 294 RBI.
Canha receives a $2 million signing bonus and salaries of $12 million next year and $10.5 million in 2023. The Mets hold an $11.5 million option for 2024 with a $2 million buyout.
He can earn $50,000 bonuses for making the All-Star team, winning a Gold Glove or a Silver Slugger award. He would get a $50,000 bonus for winning a season MVP award, $25,000 for finishing second in the voting and $10,000 for coming in third.
Canha also would receive a $50,000 bonus for being selected MVP of the League Championship Series, and $100,000 for winning World Series MVP.
"Mark is an extremely versatile player, who has an elite ability to get on base," Eppler said. "He has gap-to-gap power and can hit in any spot in the lineup."
In another move, the Mets declined to offer a contract to right-hander Robert Gsellman, making him a free agent. Gsellman was eligible for salary arbitration.
The team did tender contracts by Tuesday night's deadline to all its other arbitration-eligible players.
New York went 77-85 this season, fading to third in the NL East after a strong start.
Marte made his big league debut in 2012 with Pittsburgh and was an NL All-Star in 2016. He won Gold Gloves in 2015 and 2016 with the Pirates.
He is a .289 career hitter with 126 homers, 46 triples, 502 RBI and 296 steals over 10 major league seasons.
The 32-year-old Escobar was a first-time All-Star in 2021, when he batted .253 with 28 homers, 90 RBI and a .786 OPS for Arizona and Milwaukee. The switch-hitter has been a solid offensive contributor and a steady defender at third base the past four seasons, except for a slump during the pandemic-shortened 2020 season.
Escobar has spent most of his time at third base but has experience all over the infield, and his versatility could be important for the Mets.