Hall of Fame coach Jackson, the 11-time NBA championship winner, had been widely expected to come out of retirement to lead the Lakers for a third time but the Lakers instead opted for the offense-minded D'Antoni.
According to local media, D'Antoni, 61, has signed a three-year deal for $12 million, with the Lakers holding an option for a fourth year.
Jackson, heavily favoured to get the job, met with Lakers general manager Mitch Kupchak and executive vice president Jim Buss on Saturday. Though contractual terms were not discussed, he said, he told them he would make a final decision on Monday.
Before that could happen, though, Kupchak phoned Jackson at midnight on Sunday to inform him that D'Antoni had been appointed instead.
"He told me that the Lakers had signed Mike D'Antoni to a three-year agreement and that they felt he was the best coach for the team," Jackson said in a statement. "The decision is of course theirs to make.
"I am gratified by the groundswell of support from the Laker fans who encouraged my return and it is the principal reason why I considered the possibility."
Jackson, 67, compiled a 1,155-485 record in 20 NBA seasons, winning six NBA titles with the Chicago Bulls followed by five more in two separate stints with the Lakers.
D'Antoni, who is known for his fast-paced offense-oriented system, had a 388-339 record as head coach of the Denver Nuggets, the Suns and the Knicks.
"After speaking with several excellent and well-respected coaching candidates, (Lakers owner) Dr. (Jerry) Buss, Jim and I all agreed that Mike was the right person at this time to lead the Lakers forward," Kupchak said in a statement.
"Knowing his style of play and given the current make-up of our roster, we feel Mike is a great fit, are excited to have him as our next head coach and hope he will help our team reach its full potential."
D'Antoni is expected to be formally introduced as the 24th Lakers head coach later this week, though he has not yet been cleared to fly after having knee replacement surgery earlier this month.
While the possibility of Jackson's return as coach had thrilled Lakers players and fans, D'Antoni is held in high esteem by All-Stars Kobe Bryant and Steve Nash.
"Everyone knows how much I love Mike," said Nash, who played four seasons under D'Antoni in Phoenix.
"If he were the coach, it would be seamless and terrific for me, and I think the team as well."
Bryant, a 14-time All-Star, was a huge fan as a child of D'Antoni's basketball play in Italy, where he grew up, and later got to know him well when D'Antoni was an assistant coach on the US national team.
Spanish forward Pau Gasol, another Lakers All-Star, said the team was looking forward to their new coach's arrival.
"We're all excited to have (D'Antoni) here and learn his principles and offense and defense, and make it work for the best of us," Gasol said after practice on Monday.
"It should be a fun system to play in. There are a lot of opportunities with an up-tempo kind of game, an unselfish kind of game, too. We all look forward to working with it and exploiting the options."
D'Antoni takes over a Lakers team which is well accustomed to success and bristling with All-Stars but limped to a dismal 1-4 start this season before Brown was abruptly fired on Friday.
At that point, the 16-time NBA champion Lakers had the worst record in the Western Conference following an off-season in which the team acquired All-Star center Dwight Howard and point guard Nash, a two-time league Most Valuable Player.
Last season, the Lakers won the Pacific Division with a 41-25 record and reached the conference semi-finals before falling to eventual conference champions Oklahoma City Thunder in five games.
However, early this season they were hobbled by injuries and struggled under the much vaunted new Princeton offense installed by Brown.
Howard has been easing his way into form after back surgery that ended his 2011-12 season, Nash has missed the last five games due to a leg injury and Bryant has been slowed by a foot injury.
Ironically, the Lakers have since won their last two games under interim coach Bernie Bickerstaff, who is expected to remain in charge for Tuesday's game against the San Antonio Spurs.
D'Antoni's first game in charge is expected to be on Friday at the Staples Center in downtown Los Angeles where they will host the Suns.
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