The deal thrusts the Lakers back into the mix of contenders for an NBA title as Howard, the face of the Magic franchise and a three-time defensive player of the year, joins Kobe Bryant, Spain's Pau Gasol and Steve Nash in Los Angeles.
"Well, it looks like Superman has found a home," Bryant wrote on his Facebook page, referring to the moniker his new team-mate earned because of the red cape he wore during the NBA 2008 Slam Dunk contest.
Howard's move to Los Angeles concludes a drawn-out process during which the Magic's top scorer and rebounder for each of the last six seasons went back and forth over his decision on whether to stay with the team.
The 26-year-old center, taken first overall by Orlando in the 2004 NBA Draft, had requested a trade before the 2011-12 season but then said in March he would stick with the Magic rather than test free agency.
But last month, he reiterated his desire to be traded and said if a move was not made, he would leave the team when his current contract expires at the end of next season.
The attention on his playing future was the most directed at any prospective free agent since three-time NBA most valuable player LeBron James went on national television to announce his much-publicised move to Miami in 2010.
Orlando gets guard Arron Affalo and forward Al Harrington from the Nuggets, forward Maurice Harkless and center Nikola Vucevic from the 76ers and forward Josh McRoberts and guard Christian Eyenga from the Lakers.
The Magic, who sent guard Jason Richardson to the 76ers, will also receive five draft picks, including three first-rounders, over the next five years.
"A primary goal for our basketball team is to achieve sustainability while maintaining a long-term vision," Orlando General Manager Rob Hennigan said in a statement. "We feel this deal puts us in a position to begin building in that direction."
The departure of Howard comes nearly three months after the Magic fired head coach Stan Van Gundy and mutually parted ways with General Manager Otis Smith.
Van Gundy had also clashed with Howard last season, at one point saying that his top player had wanted him fired.
In addition to Howard, the Lakers get guard Chris Duhon and forward Earl Clark from Orlando.
It is the second offseason splash made by a Lakers team that has suffered two straight early playoff exits since capturing a 16th NBA title in 2010. The team added two-time NBA MVP Nash last month in a deal with the Phoenix Suns.
Philadelphia get twice NBA champion center Andrew Bynum from the Lakers and Denver land forward Andre Iguodala from the 76ers, who posted a "Thank You, Andre" message on their website with a photo of their former player soaring to the rim.
Iguodala, who has averaged 15.3 points and 5.8 rebounds per game during an eight-year career spent entirely with the 76ers, will be counted on to help a Nuggets team that fell in the second round on the 2012 NBA playoffs.
"It's not often you get the opportunity to improve your team by adding an All-Star player like Andre Iguodala," said Nuggets Vice President of Basketball Operations Masai Ujiri.
"He's an Olympian, a great defender and a great all-around player. We think he fits in really well with the type of system coach George Karl runs and the team we have here in Denver."
Gasol expressed surprise when told of the Bynum and Howard trades ahead of Spain's Olympic semi-final against Russia in London on Friday.
"I want to wish Andrew the best with his new team and stage, and I'm excited, very excited about our team," he said.
"I think it's something that puts us in a position of being an extremely powerful team, and a team with all the chances to go for the (NBA) ring."