Vincent, who helped the Miami Heat reach the NBA Finals this spring, will earn $33 million for the contract, which can be signed starting Tuesday.
The 6-foot-3 guard started all 22 games in the playoffs for the Heat, shooting 37.8% on three-pointers on more than six attempts per game. He averaged 9.1 points and 2.5 assists while shooting 33.4% from deep during the regular season.
Prince became available when the Minnesota Timberwolves declined to guarantee his $7.4-million deal earlier this week.
A 6-7 forward, he shot 38.1% from three-point range last season. The sides are still working on the details of the contract, which can’t be signed until Tuesday, but it’s expected the Lakers did not use any of their midlevel exception in the deal.
Prince, 29, has played seven seasons in the NBA and averaged 9.1 points, 2.4 rebounds and 1.6 assists in 22 minutes a game last season. He shot 46.7% from the field and 84.4% from the free-throw line.