At the same time, Christie said, he and Sweeney have worked to find common ground on appointments.
"Today, we find that common ground with Chief Justice Rabner," Christie said.
Sweeney, speaking after Christie, called the agreement an "enormous win," and a decision that would "eliminate the uncertainty that's going on in our justice system."
After praising Solomon, Sweeney said: "We couldn't have come up with a better deal."
Rabner's reappointment, which would gain him tenure, was hailed by liberal-leaning advocacy groups and the state bar association, which has accused Christie of attacking judicial independence.
In 2010, Christie did not renominate Justice John Wallace - the first time in modern history that a sitting New Jersey justice had been denied tenure.
The decision - which Christie said was under his prerogative to remake the court - set off a war with Democrats, who have since blocked most of Christie's court appointees.
Christie, meanwhile, denied reappointment last year to a second justice, Republican Helen Hoens.
The situation has resulted in two vacancies on the seven-member court; Rabner has responded by calling up appellate court judges. Solomon, if confirmed, would fill one of the two vacancies.
Christie - whose nominations to the court made in the prior legislative session have expired - said Wednesday that he was "not at this time considering another name" to fill the remaining vacancy.
"It took us long enough to get to these two," Christie said. "Revel in the enjoyment of the moment, everybody."
Rabner, 53, has served on the court since 2007. Once confirmed by the Senate, he will be able to serve until the mandatory retirement age of 70.
Solomon's nomination is also contingent on approval in the Senate. A former Republican lawmaker, he was named deputy U.S. Attorney for the southern vicinages of New Jersey in 2002, while Christie was U.S. Attorney.
As governor, Christie appointed Solomon - who served as a state Superior Court judge in Camden County for several years after leaving the U.S. Attorney's Office - to his cabinet in 2010, naming him president of the state Board of Public Utilities.
In 2011, Christie nominated Solomon to again become a Superior Court judge. Christie later named Solomon's wife, Dianne, to head the Board of Public Utilities.
On Wednesday, Christie said he was "glad to have the opportunity to nominate someone I know so well, for a position I consider to be so important."
If, as expected, Solomon is confirmed, he will be the second member of the high court from Camden County. Former Superior Court Judge Faustino J. Fernandez-Vina, a Barrington resident, was sworn in in January, replacing Hoens. Two justices are from Morris County.
Rabner has drawn Christie's ire, including over a decision he authored last year that prevented Christie from disbanding the state's affordable-housing agency.
Rabner also wrote the strongly worded decision that paved the way for the legalization of same-sex marriage. Under his tenure, the court has also upheld a school-funding formula denounced by Christie.
At a town-hall event earlier this year, Christie attributed property tax levels to the school-funding decisions. Describing efforts to change the court, he had said he would "have another opportunity coming up in June" with Rabner's reappointment.
On Wednesday, Christie - who led the U.S. Attorney's Office while Rabner was a federal prosecutor under him - said his criticisms of the court had been misconstrued as signs related to his decision on Rabner. He noted his past support for Rabner, including before Rabner's initial appointment to the Supreme Court by Gov. Jon S. Corzine.
Christie said there wasn't a "louder, stronger voice seven years ago" for Rabner to become chief justice, he said. "My respect for him has never been diminished."
Rabner, who along with Solomon was at the news conference, said he was "grateful" for the renomination, "both personally, and . . . on behalf of the institution of the judiciary that I care so deeply about."
The New Jersey Bar Association - which along with the 21 county bar associations had called for Rabner's renomination - billed Christie's announcement in a statement as a "resounding victory for judicial independence." The association had warned of a chilling effect if judges thought that they had to decide cases in line with a governor's wishes to gain tenure.
Christie said Wednesday that the quality of a justice's decisions was "just one factor" to consider in renominations.
"This judicial independence thing is a crock," Christie said. "It's a complete crock. And the bar association knows it." He blasted the association as a "self-congratulatory group" that "struggles for relevance."
Christie said he would "reserve the right to exercise the authority given to me under the constitution" to not grant tenure to judges.
Though Democrats have blocked past nominees, Christie said "nearly half the court has been changed" under his tenure, noting that three of his picks - all Republicans - did win confirmation from the Senate.
The partisan balance of the court has traditionally been split 4-3, generally in favor of the governor's party.
Solomon, if approved, would be the third Republican justice on the court, which also has two Democrats and an independent.
His selection and Rabner's renomination are "a very, very positive step forward from the last three or four years of really negative impact on the New Jersey judiciary," said Robert Williams, a law professor at Rutgers-Camden who studies the court.
It would have been a "nail in the coffin" of judicial independence if Rabner had not been renominated, Williams said. Of the stalemate over the court, "it remains to be seen whether the damage will persist, or whether it will kind of fade into history," he said.