All four players were eligible for salary arbitration.
Oakland also finalized an $8.1 million, two-year deal with reliever Grant Balfour. The sides agreed to terms Friday pending a physical.
Willingham receives $6 million for the 2011 season, Kouzmanoff $4.75 million, Braden $3.35 million and Jackson $3.2 million.
Reliever Craig Breslow, Oakland's lone remaining arbitration-eligible player, asked the A's for $1,550,000 while the club offered $1,150,000. Breslow earned $425,000 last season, when he went 4-4 with a 3.01 ERA in 75 appearances.
The A's acquired Willingham in a trade last month with Washington for a pair of prospects. He is expected to start in one of the corner outfield spots.
Braden, an 11-game winner in 2010, became a national name after pitching a perfect game May 9 against Tampa Bay -- the franchise's first since Hall of Famer Catfish Hunter did it in 1968.
Willingham batted .268 with 16 home runs and 56 RBIs last season, his second in Washington after five years with Florida.
He is expected to give the A's a solid middle-of-the-order presence along with newly acquired slugger Hideki Matsui and David DeJesus, who came to Oakland in a trade with the Kansas City Royals in November.
The A's hit just 109 homers and scored 663 runs last season, their second fewest in the last 28 non-strike seasons.
The 31-year-old Willingham finished last season on the 60-day disabled list as he recovered from surgery on his left knee. He was sidelined after Aug. 15 and played 114 games, 108 of those in left field.
Jackson underwent surgery for a sports hernia in early September and didn't play again. Acquired from Arizona last June 16, he batted .228 with one home run and five RBIs in 18 games for Oakland. He hit .236 with two homers and 16 RBIs in 60 games overall.
The 33-year-old Balfour went 2-1 with a 2.28 ERA in 57 appearances for the Rays last season, his seventh year in the big leagues.
Balfour will earn $3.75 million next season and $4 million in 2012. The deal includes a $4.5 million club option for 2013 with a $350,000 buyout.
Balfour is happy to have found his spot less than a month before pitchers and catchers report to spring camp -- and thrilled that his father, David, is in remission from a rare form of cancer after surgery and treatment last year.
For Balfour, this is a new start. He hopes to continue in a setup role he had with the Rays.
"I thought it was very similar to where I've come from, a young rotation with a lot of upside," Balfour said. "Looking at the team we've got I think we have a good chance to compete in the American League West and have a good chance to win it. ... I'm hoping my job will be similar to what I had been doing in setup role and pitching in close games. I thrive and love pitching in those games."