The two sides are now in negotiations on a contract.
The Lakers made Scott a verbal offer on Thursday after Scott spoke with owner Jim Buss. Scott and his representatives are reviewing the Lakers' offer.
Scott, a former Lakers star who won three titles playing next to Magic Johnson, has long been the front-runner for the job.
The Lakers have been without a coach since Mike D'Antoni resigned at the end of April. Scott interviewed for the job three times, but the organization prioritized the draft and free agency over hiring a coach.
Scott received a key endorsement from Lakers star Kobe Bryant, who played with Scott as a rookie in 1996 and has maintained a close relationship with him since.
Information from ESPN.com's Ramona Shelburne was used in this report.
Lakers Offer Head Coaching Job To Scott
Chris Broussard discusses the Lakers' decision to offer their head coaching position to Byron Scott.