Rodriguez's deal, worth $37 million plus additional incentives, is pending a physical, which the New York Post reported will take place Wednesday.
"I feel good where we are today, compared to where we were yesterday," Mets GM Omar Minaya said Tuesday. "I'm going to stay positive. But total completion of the deal is when everything is signed, sealed and delivered, and [right now] we continue to have dialogue. That's the best I can tell you."
The deal is a one-year increase over the two years and $24 million the Mets are said to have initially offered the closer, who broke the major league single-season saves record last season with 62.
The agreement was reached Tuesday about 5 a.m., but the contract probably won't be finalized until next week at the earliest.
"Tired today," Minaya said. "We have a lot of stuff going on."
Rodriguez saved 62 games for the Los Angeles Angels this year, five more than the previous big league mark set by Bobby Thigpen of the Chicago White Sox in 1990, and then filed for free agency. Rodriguez's agent, Paul Kinzer, had hoped to get a five-year contract, possibly equaling the $15 million average salary Mariano Rivera is earning from the New York Yankees.
But with baseball executives worried about the national recession, Kinzer accepted a more modest deal. The Mets were a natural fit because they were one of the few big-market teams looking for an elite closer this offseason.
All-Star Billy Wagner is expected to miss all of next season following elbow ligament replacement surgery.
"The way that we lost so many close games late, I think that was critical for us to -- theoretically -- address this thing here. We have addressed it very well," manager Jerry Manuel said, laughing. "I mean, they say the word on the street is good. It's good. That's just the word on the street. We've got to get it written down."
K-Rod could fit in with New York in another way, too. Some take exception to his antics on the mound, and the Mets have drawn the ire of opposing teams for their boisterous celebrations.
The fact that several free-agent closers were available probably drove down Rodriguez's market value. Coming off its second consecutive September collapse, New York got a boost as it prepares for its first season at Citi Field, an $800 million ballpark built adjacent to Shea Stadium.
With the agreement, the Mets are ceasing negotiations with Brian Fuentes and career saves leader Trevor Hoffman, two other free-agent closers, one of the people said. Rodriguez's contract will contain an option for 2012 that could become guaranteed based on his performance, the person said.
"He's a competitor. That's why he's one of the guys that we've been looking at," Minaya said.
The Mets still have a hole in their rotation and a shaky setup situation, however. So Minaya knows he might have more work to do on the bullpen.
"We have to find ways to change it up a little bit, find ways to have a different look to what we do back there," he said. "We're going to look at some free agents and we're going to look at that through some trades. I don't feel that we should just tell ourselves the only thing we need is one guy."
As for finding a starter, Minaya said he probably would meet with Oliver Perez's agent, Scott Boras, before the winter meetings end on Thursday. Perez, a free agent, was acquired by the Mets in 2006 and went 10-7 with a 4.22 ERA in 34 starts this year.
Minaya also said he had spoken to the agent for Pedro Martinez, who spent the past four seasons with the Mets.
Rodriguez, a three-time All-Star who turns 27 next month, was regarded as the premier closer on the market. While some teams were worried about his violent pitching motion and drop in velocity last season, he developed an outstanding changeup to go along with his other pitches.
"A very confident young man. He's an exciting guy to talk about," Manuel said. "Anytime you acquire a person at that level, it raises the level of everybody else. It's almost the same as saying Johan [Santana]) is pitching. You see a different spirit with your team. To have a guy, a guy of that sort at the end of a ballgame, is very important, very critical for us. Or for anybody."
Rodriguez and Kinzer arrived in Las Vegas last weekend and dined Sunday night with Minaya, chief operating officer Jeff Wilpon and other team officials at a steakhouse. Turns out, it didn't take long to reach an agreement.
In a slow free-agent market, Rodriguez was the first of the top-tier free agents to reach an agreement. Starting pitchers CC Sabathia and A.J. Burnett, first baseman Mark Teixeira and outfielder Manny Ramirez are among the high-profile players still searching for deals.
Information from ESPN.com's Jerry Crasnick and The Associated Press was used in this report.