"The Maloof family’s interest in purchasing the Kings, Monarchs, and ARCO Arena originated in 1997 when they contacted then-Managing General Partner Jim Thomas regarding the availability of the teams and arena. On January 14, 1998, the Maloofs completed the purchase of a minority limited partnership in the organization’s franchises and ARCO Arena. Although both the Kings and Monarchs suffered through subpar seasons in 1997- 98, the Maloofs continued their pursuit of primary ownership and on January 15, 1999, subsequently purchased controlling interest, effective July 1, 1999. The NBA Board of Governors unanimously approved the ownership transfer on May 7, 1999, in New York, at which time the Board of Governors appointed Joe Maloof to the Board. The official closing of the ownership transaction took place on July 1, 1999."
From the kings.com bio -- they had been pursuing it for a year, completed the purchase by January (before the season began in that short year), and it was just the official paperwork that took till May/July.