General manager Dave Stewart thinks Greinke is the type of pitcher who can perform at a top level into his upper 30s.
"He's got great mechanics," Stewart said Tuesday. "He doesn't exert a lot of energy doing his job and he's an athlete. He works hard, keeps himself in great condition, and when those things are happening, and when an athlete takes advantage of those things, it makes it a whole lot easier in the latter part of your career."
"I'll be a testament to that," he added.
Stewart was a 20-game winner in four straight seasons from age 30 to 33, going 84-45 with a 3.20 ERA for Oakland. He then went 44-45 with a 4.94 ERA over his final five seasons with the Athletics and Toronto.
Arizona announced Greinke's contract Tuesday, four days after reaching an agreement and a day after the pitcher took his physical.
On Tuesday night, the Diamondbacks agreed to acquire All-Star right-hander Shelby Miller from the Atlanta Braves for overall No. 1 draft pick Dansby Swanson, outfielder Ender Inciarte and pitching prospect Aaron Blair, sources have confirmed to ESPN.
Greinke's $34.4 million average salary is the highest in baseball history, topping the previous mark of $31 million set last week when left-hander David Price agreed to a $217 million, seven-year contract with Boston. Greinke signed a $147 million, six-year deal with the Dodgers in December 2012 that included an opt-out clause. He went 51-15 during his three years with the Dodgers and will wind up earning $282.5 million over nine seasons.
Out of the playoffs since 2011, the Diamondbacks finished 79-83 last season -- an improvement of 15 wins from 2014. Stewart said talks with Greinke began on Thursday night, and Arizona ownership gave the go-ahead Friday. Negotiations culminated in an agreement later in the day, pending a successful physical.
Before the trade for Miller became known, Stewart said Arizona has talked with the agent of free-agent pitcher Mike Leake and also said the Diamondbacks discussed the possibility of acquiring Miami Marlins ace Jose Fernandez.
"If you've got an opportunity to get that type of pitcher, you definitely have to talk about it," Stewart said.
To clear a roster spot for Greinke, right-hander A.J. Schugel was designated for assignment.
Information from The Associated Press was used in this report.