Ballmer said Lawrence Frank, the team's executive vice president, will assume responsibility for basketball operations. Frank also will oversee general manager Dave Wohl.
Both Rivers, 55, and Frank, 46, will report directly to the owner.
"Doc knows how to win championships," Ballmer said in a news release. "That is what we prioritize, and that is what Doc will focus on. He is key to integrating our new players with our returning players and taking us to new heights on the court."
Rivers will continue to have a strong voice in personnel and organizational matters and will partner with Frank, Ballmer later told ESPN on Friday.
Oakley was arrested and charged with five misdemeanors -- two for assault, two for harassment and one for trespassing -- in the altercation in which security physically removed him from the arena at the start of a Feb. 8 game. The incident stemmed from a longstanding dispute Oakley had with Knicks owner James Dolan.
Oakley, 53, admitted no wrongdoing but agreed to stay away from Madison Square Garden for one year as part of the deal. The charges will be dismissed if Oakley stays out of trouble for six months and adheres to the ban.
"Jason and his representatives reached out to us regarding his desire to sign one last contract with the team in order to retire as a Detroit Piston," general manager Jeff Bower said in a statement. "Jason made an impact on and off the court with the organization, spending eight seasons in Detroit, many with deep playoff runs. We're pleased that Jason has chosen to remain connected to our organization and wish him well in the future."
Drafted 26th overall by Detroit in the 2005 NBA Draft out Cincinnati, the 6-foot-7, 260-pound Maxiell spent eight seasons with the Pistons, averaging 6.1 points, 4.4 rebounds and 19.1 minutes in 523 games. The Chicago native was a part of four playoff runs from 2005-08, including three Eastern Conference finals appearances. He averaged 4.7 points, 3.3 rebounds, and 16.6 minutes in 35 career playoff games.