The Mets dealt relievers Heath Bell and Royce Ring to the Padres in exchange for the two players, who could be complementary pieces in the club's makeup.
Minaya said the deal was one explored in various phases leading into the July 31 trading deadline this year, before both clubs agreed to revisit negotiations at the General Managers Meetings, which are being held this week in Naples, Fla.
"It may not be a sexy trade," Minaya said in Florida. "You have to remember, the little ones are what count sometimes. Those are the ones."
Johnson, 25, played in 58 games for San Diego in 2006, batting .250 with four home runs and 12 RBIs.
The Padres' Minor League Player of the Year in 2005, Johnson was ranked as the Padres' No. 4 prospect by Baseball America before the 2006 season. Johnson also played in 51 games with Triple-A Portland of the Pacific Coast League and had been viewed as a player who could break out for San Diego in 2007.
"Ben Johnson is a versatile outfielder who can play all three spots, has speed and shown some power," Minaya said in a statement. "He is just 25 years old, and we feel he has yet to reach his potential.
Adkins, 29, was 2-1 with a 3.98 ERA in 55 games for San Diego last season, allowing 55 hits and 26 runs in 54 1/3 innings, walking 20 and striking out 30.
"Jon Adkins has had success on the Major League level and can pitch multiple innings," Minaya said. "He's another quality arm to add to our bullpen staff."
A member of the 2005 World Series champion White Sox, Adkins would figure to pitch in the middle innings for New York's relief corps, helping to lessen the impact of losing Bell and Ring, plus any contributors who may leave via free agency.
The Mets have had contact with the representatives for reliever Chad Bradford and remain optimistic an agreement will be reached, though the returns of free agents Roberto Hernandez, Guillermo Mota and Darren Oliver -- who teamed to pitch middle and late innings for the Mets in the second half last season -- appear less certain.
Bell -- who had been the longest tenured member of the Mets organization, signing as an undrafted free agent in 1998 -- and Ring made small contributions to the Mets' 2006 campaign.
The 29-year-old Bell had no record and a 5.11 ERA in 22 games for New York and was shuttled between the Major Leagues and Triple-A in five separate transactions, appearing in 30 more contests for Norfolk.
Ring, 25, had no record and a 2.13 ERA in 11 games for the Mets but was selected as an International League All-Star at Triple-A Norfolk, where he was 2-2 with 11 saves and a 2.97 ERA in 36 games, including a franchise record 26 2/3-scoreless-innings streak from April 19 through July 8.
The moves came as Minaya continues to be an impact figure at the General Managers Meetings. On Tuesday, Minaya announced that the Mets had reached contract agreements with free agents Orlando Hernandez and Jose Valentin.
The deal marks the second consecutive season that Minaya and the Mets have found a match for an offseason deal with the Padres. On Nov. 15 of last year, New York shipped outfielder Mike Cameron to San Diego for outfielder Xavier Nady.
Bryan Hoch is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.