The infielder, who was acquired by the D-backs on Sunday from the Blue Jays, won World Series titles wearing the uniforms of the Angels (2002) and Cardinals (2006).
"Let's hope that trend continues," Eckstein said after donning his Sedona Red uniform for the first time. "That would be nice."
Arizona manager Bob Melvin wasted little time in putting Eckstein to work, sticking him in the No. 2 spot in the lineup at second base on Monday.
A shortstop throughout most of his eight-year career, Eckstein has appeared in six games at second this year as well as 14 back in 2001. The D-backs are without the services of starting second baseman Orlando Hudson, who suffered a season-ending wrist injury earlier this month.
"I'm very excited about the opportunity to be playing second now," he said. "I figured that would probably be a position I'd end up playing at the end of my career."
It's a position that Eckstein played throughout his Minor League career as well.
The 33-year-old arrived in Phoenix around 10:30 p.m. MST Sunday and was at the ballpark ready to go by 9 a.m. on Monday. Eckstein went from a team playing out the season's final month to one locked in a battle with the Dodgers for the National League West crown.
"Having an opportunity to come to this club is a blessing," he said. "I thank the Blue Jays for putting me in this situation and [I'm glad] that the Diamondbacks wanted me. Having that opportunity, that's why you play the game, to win world championships."
Eckstein has appeared in four postseasons during his career and is a career .333 hitter in the World Series. That includes a .364 mark in 2006, when he won the World Series Most Valuable Player as a member of the Cardinals.
Ironically, it's the Cardinals that he will face in his first game for the D-backs. In fact, he found himself staying at the same hotel as his former mates and gave a couple of them a lift to the ballpark Monday.
When asked about what he liked best about his new team, he didn't hesitate.
"The pitching staff," Eckstein said. "Having the opportunity to compete for a world championship. You look at the arms they have, every single day you have a great chance to win. Great young ballclub. They did great things last year. Hopefully we can build upon it this year."
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.