It took Billy Beane to get things moving.

The Cleveland Indians stepped up with an uncharacteristically big offer to land Edwin Encarnacion as a free agent. But it took a late push from the Oakland A's head honcho to get things moving and push the Indians' negotiations over the top.

Encarnacion's agent, Paul Kinzer, told ESPN.com that the agreement came together quickly Thursday night, and that the Athletics and Texas Rangers were in the running to sign Encarnacion until the "last minute."

"Billy made this tough," Kinzer said. "It was a hard decision. He really got creative and came on strong down the end and really made a push. Edwin turned down more money, and it came down to Cleveland being closer to home [in the Dominican Republic].

"The one thing I'll give Billy: When he jumped in, he jumped in with both feet and really jump-started the process. He wasn't just flirting -- he was dating."

Kinzer confirmed reports that Encarnacion's contract with Cleveland is for three years and a guaranteed $65 million, including a $5 million buyout. The contract has a $25 million club option for 2020 that could bring the overall value of the agreement to $85 million.

Encarnacion is currently at home in the Dominican and is hoping to travel to Cleveland early next week to complete his physical exam and finalize the deal, Kinzer said.

Encarnacion ranks second to Baltimore's Chris Davis among MLB hitters with 193 home runs since 2012. As such, he was the premier free-agent slugger on the market this offseason. But several factors might have helped to suppress his value to potential suitors.

Encarnacion turns 34 in January, and since Toronto gave him a qualifying offer in November, Cleveland had to forfeit its first pick in the 2017 first-year player draft (No. 25 overall) in exchange for signing him. With Mark Trumbo, Jose Bautista, Chris Carter and Mike Napoli among the other sluggers still available, the Indians and other teams in search of power also had an abundance of options this winter.

Toronto gave Encarnacion a four-year, $80 million offer early in the offseason, but he turned it down because he thought he could do better. The Blue Jays then filled their designated hitter void by signing Kendrys Morales to a three-year, $33 million contract. Background interviews with Encarnacion's camp and Toronto's front office have revealed some disagreement over how doggedly the Jays were pursuing Encarnacion as the offseason progressed.

Kinzer also characterized published reports of Encarnacion's contract demands as inflated. He denied that Encarnacion had told clubs it would take a five-year, $125 million investment to sign him.

"That never came out of my mouth for one team,'" Kinzer said. "My only statement was, 'The market will dictate the years and the salary. We know where we would like to get.'"

As decision time neared, Encarnacion had to choose among several shorter-term options. An MLB source said Oakland's proposed offer was for two years and $50 million. The deal included a first-year opt-out for Encarnacion and a third-year club option.

When the Indians transaction was completed Thursday, Kinzer was at a Six Flags amusement park with his grandchildren, and Indians president of baseball operations Chris Antonetti was attending a performance of "The Nutcracker Suite" with his family. Shortly thereafter, Encarnacion came to grips with the realization that he would be leaving Rogers Centre -- his baseball home since 2009 -- to embark on a new chapter at Progressive Field.

"Edwin loved the city, and he loved the fans," Kinzer said. "[Toronto] was home for him. This was tough for him. He was emotional.

"Cleveland knocked them out in the playoffs, so he knows that team well. He's friendly with a lot of people on that team. The one thing he'll have to get used to is being out of a dome in April."