According to a team spokesman, the former Florida standout is expected to sign with the team over the next few days with a small guarantee.
On Sunday, Frazier's agent, Matt Ramker of ASM Sports, tweeted, "Congrats to Michael Frazier II @mfrazier20 on agreeing to terms with the LA Lakers. Great things on the horizon. #GatorNation #LakersNation."
The 6-foot-5 guard averaged 12.1 points and 1.4 assists a game with Florida, shooting 48.2% from the field and 38% from three-point range.
"Lakers are getting one of the best rookie shooters and a tremendous worker," Ramker tweeted. "Don't need an apartment, Michael Frazier sleeps in the gym."
A person privy to the details of the agreement, but not authorized to comment publicly, said Frazier will sign a two-year, minimum-salary deal of $1.4 million ($525,093 and $874,636, respectively).
Only $50,000 of his first-year salary will be guaranteed.
Frazier will be the 16th player on the roster, one over the regular-season limit. The Lakers recently signed Texas forward Jonathan Holmes to a similar deal, but with a $100,000 guarantee.
Second-year players Tarik Black and Jabari Brown have non-guaranteed contracts for the 2015-16 season at $845,059 apiece.
Should Frazier not make the cut with the Lakers, he could become an affiliate player in the
The Lakers have also been linked to Robert Upshaw, but have no immediate plans to sign the former Washington and Fresno State center.
MORE ON THE L.A. LAKERS: