The Kings had been considering a move to Anaheim, Calif., after several failed efforts to build a new arena in Sacramento, but they decided to give Johnson one more shot.
"The mayor of Sacramento has told the NBA relocation committee that he will have a plan for a new arena within a year," co-owner Joe Maloof said Monday. "If not, the team will be relocated to another city."
The Kings had until Monday to let the NBA know whether they would seek permission to move. Johnson, a former NBA star, had spent the past few months doing his best to keep Sacramento's only major sports team. He arranged $10 million in sponsorship pledges from the corporate community and overcame seemingly long odds to succeed.
"This is one of the proudest moments of my life because the community believed when no one else did," Johnson said. "We kept believing. And if you believe, anything is possible."
A feasibility study for a new arena in Sacramento is scheduled to be completed this month. There has always been a divide between Kings fans and the broader public on how to finance a facility.
Four California lawmakers, including the leader of the state Senate, sent a letter to NBA Commissioner David Stern last week pledging to work with local leaders over the next year to try to build a sports and performing arts complex to replace the Kings' outdated arena.
The team said that if an arena plan is not finalized in a timely fashion, the NBA's relocation committee has assured the Kings that it would support a move to another market for the 2012-13 season.
RATINGS UP: Television viewership for the NBA playoffs is up 30 percent from last season.
First-round games were watched by an average of more than 4.15 million people, up from fewer than 3.2 million last year.
To this point of the playoffs, TNT has drawn the highest average rating ever for games on cable. ESPN's first-round ratings were the highest since it began televising the playoffs in 2003, and ABC's were the best since 2004.