Boras and K-Rod had met face-to-face before and after last Thursday's Mets game at Dodger Stadium.
"He contacted us several weeks ago, and we met him in L.A. and he signed up with us," Boras told ESPNNewYork.com during a National League All-Star media session at the Arizona Biltmore.
Rodriguez, 29, is in the final guaranteed season of a deal that pays at least three years, $37 million and was negotiated by former agent Paul Kinzer.
If Rodriguez finishes 55 games this season, a vesting option for $17.5 million kicks in for 2012. Otherwise, K-Rod receives a $3.5 million buyout in addition to his $11.5 million salary for this season.
Because Rodriguez likely is in his final contract as a Met, the only issue for the organization is whether Boras would hold up a trade should the Mets attempt to deal the closer to one of the 10 teams on his no-trade list.
Boras indicated Rodriguez would not be inclined to accept a trade to a place where he would serve in a setup role if the club is on K-Rod's no-trade list.
"This man is built to be a closer," Boras said.
Agents often use no-trade protection to stall trades until extra years or other financial incentives are provided. In Boras' case, however, he rarely agrees to extensions during exclusive negotiating windows because he can maximize the value of a new contract in open bidding during an offseason.
Rodriguez's 10-team no-trade list is not publicly known, but a baseball executive told ESPNNewYork.com it was submitted at the beginning of the three-year contract and does not fluctuate year to year.
Boras said he intended to discuss with general manager Sandy Alderson and his new client what might be palatable in a trade if the organization is on the protected list.
"This is something that Sandy and Frankie and I will talk about," Boras said.
Boras used the word "historic" to describe Rodriguez's value.
"I think the main thing with players, the greatest security they have is their performance," Boras said. "And Frankie, at the age of 29, he's ahead of all closers in history, really, with the amount of saves he's amassed. He's got a remarkable record. He's in good shape. He's performing well. And so I just think you begin with that dynamic about how you begin with these scenarios."
Adam Rubin covers the Mets for ESPNNewYork.com.