The two sides have agreed to a four-year deal worth more than $9 million, including a team option in the fourth season, according to the source.
An official announcement will come Friday after the Kings' sale to Vivek Ranadive closes.
Malone's hiring officially ends Keith Smart's tenure as Sacramento's coach. Smart took over for the fired Paul Westphal in January 2012 and had one year remaining on his contract.
NBA coaching sources maintain that Malone was the only coaching candidate considered by Ranadive, who became familiar with Malone as a Warriors minority owner.
A source close to the situation told ESPN The Magazine's Chris Broussard that legendary player and general manager Jerry West, now a consultant with the Warriors, has been counseling Ranadive through the hiring process. Ranadive is in the process of interviewing GM candidates, including Chris Wallace and Travis Schlenk.
Malone is the son of former NBA coach Brendan Malone. Mike Malone was previously the top assistant to Monty Williams in New Orleans and Mark Jackson in Golden State. It was with Golden State that Ranadive became familiar with Malone, and he was impressed enough to take the unusual step of hiring a coach before hiring a new GM.
Brendan Suhr, who served as an assistant coach with Malone's father on Chuck Daly's staff in Detroit, took to Twitter on Thursday evening to congratulate Malone.
"Congrats to Mike Malone on becoming HC of Sac Kings His Dad Brendan & I were C Daly's asst w/ Bad Boys. He has paid his dues. Proud of him," Suhr tweeted.
Malone was also one of the early candidates for the Los Angeles Clippers job.
Williams, who hired Malone in New Orleans despite never having worked with him before, told ESPNLosAngeles.com last week that, "I hope that he gets a job soon. I know he really wants to do it, and I know he'll be a really good head coach. The tough part is knowing I gotta coach against him because I know he really knows his stuff.
"Mike was always a good sounding board, he wasn't afraid to stand up for what he believed in."
Information from ESPN.com's Marc Stein, ESPN The Magazine's Chris Broussard and The Associated Press was used in this report.