SARASOTA, Fla. >> David Ortiz wants to finish his career with the Boston Red Sox.

“I love playing the game. I love being part of this organization, and knowing that you’re going to finish your career here,” the 38-year-old said Monday. ‘It’s something that’s a huge accomplishment.”

Due $15 million in 2014 in the final season of a two-year deal, Ortiz agreed Sunday to a new contract that calls for a $16 million salary in 2015 and could be worth up to $48 million over three years.

Ortiz’s contract includes a $10 million club option for 2016 that could escalate to $16 million and become guaranteed, and a club option for 2017, also at $10 million to $16 million.

“This is the place I want to be,” the 38-year-old designated hitter said. “This is the place that I know.”

Ortiz said the agreement will make him “stress less.”

A nine-time All-Star during 11 seasons with Boston, Ortiz has 431 major league homers. Big Papi and the Red Sox have spent a lot time discussing his future — one year at a time.

“I guess you guys get tired of me talking about contracts all the time,” he said. “At least I’m going to have some time off from answering questions dealing with the contract situation.”

Ortiz’s 2016 option would become guaranteed at $11 million if he has 425 plate appearances the previous year and passes a team physical. If he passes the physical, it would become guaranteed at $12 million for 475 plate appearances, $13 million for 525, $14 million for 500 and $15 million for 575. If he has 600 plate appearances, it would become guaranteed at the higher of $16 million or the qualifying offer price for free agents — the average of the top 125 major league contracts by average annual value.

If Ortiz doesn’t pass the physical, the 2016 club option price would be the midpoint of $10 million and the figure for whatever threshold he reached.

The 2017 club option would escalate at the same prices and thresholds as the 2016 vesting option.

Ortiz was MVP of last year’s World Series, when Boston won its third title in 10 years. He batted .309 with 30 home runs and 103 RBIs last season after returning from a strained right Achilles tendon that limited him to 90 games in 2012.

“This virtually guarantees that David will finish his career with the Red Sox,” general manager Ben Cherington said. “It means that David will be in the middle of the lineup for longer.”

If Ortiz plays through 2017, he would be nearing his 42nd birthday.

“In a lot of different ways, David is an outlier. He’s an exception to the rule,” Cherington said. “There are just not many guys who produce at the level he has at this point in their career.”

Ortiz was reminded that only Ted Williams was as productive as he was this late in a Red Sox career.

“I know what I need to do to continue to be successful,” Ortiz said. “There’s going to be the day when I don’t feel like doing what I normally do, and when that happens, everybody’s going to know it. I feel hungry. Winning is good. I feel hungry.”

Ortiz is one of only a handful of fulltime designated hitter, with many teams preferring to have different players share at-bats.

“American League teams are doing that because they don’t have David Ortiz,” Cherington said. “At some point in the future, he doesn’t feel like he can do what he’s been doing, but we don’t see that time is coming any time soon.”