Chris Haynes of Yahoo Sports reported the deal is worth $6 million total.
This comes after the Golden State Warriors renounced the 26-year-old's rights following the sign-and-trade for All-Star guard D'Angelo Russell.
Cook served as backcourt depth behind Stephen Curry and Klay Thompson, making 28 starts during his time in the Bay Area. He is coming off a season in which he averaged 6.9 points in 14.3 minutes per game.
Most notably, he hit 41.8 percent of his three-point attempts during his two seasons with the Warriors.
Although he may not have put up major numbers, he earned the respect of head coach Steve Kerr, who told Mark Medina of the Bay Area News Group in April 2018 that Cook was "one of the most professional people I've ever been around":
"His talent is obvious. He's a great shooter. But it's his character, work ethic and what his teammates think of him that really stands out. He's one of those guys that gets it. He understands the value of hard work, the value of staying ready and producing when we call upon you and not complaining and supporting everyone else when we don't. But not everybody is like that."
While the Warriors initially made Cook a qualifying offer, they had to rescind it for salary-cap reasons, as ESPN's Bobby Marks noted:
Bobby Marks @BobbyMarks42
Pulling the Quinn Cook $1.9M QO was a necessity because of the $138.9M tax apron. Even with Shaun Livingston off the roster, GSW is restricted to signing only both second-round picks and one minimum contract. With 14 players under contract, GSW would be $215K below the apron.
That has led him to move on to L.A.
On the heels of Kawhi Leonard's decision to join Paul George and sign with the Los Angeles Clippers, as reported by ESPN's Adrian Wojnarowski, the Lakers are now focused on filling out their roster around LeBron James and Anthony Davis.
General manager Rob Pelinka seems especially intent on surrounding his stars with capable shooters.
Danny Green announced late Friday night that he was signing with the Lakers, and Wojnarowski later reported that he had agreed to a two-year, $30 million deal.
While Green is a higher-profile signing than Cook, it looks as though Cook may be poised to play a huge role next season.
He is the only point guard on the Lakers' roster, meaning he may be a starter alongside James, Davis, Green and Kyle Kuzma. If that is the case, look for Cook's production to see a significant jump.
If he can maintain his three-point shooting percentage in an even greater sample size, he will be a major weapon for a Lakers team that is already studded with stars.