The deal -- one of several made by the Lakers on Tuesday -- is for one season, according to Frazier. Anthony's agent, Aaron Mintz of CAA Sports, completed the agreement with Lakers general manager Rob Pelinka on Tuesday.
Anthony, who moved up to No. 10 on the NBA's career scoring list last season, rehabbed his career in two seasons in Portland after being out of the league for a year following an ill-fated stint with the Houston Rockets.
The 18-year veteran flourished in a bench role with the Blazers last season, averaging 13.4 points in 24.5 minutes per game while shooting a career-best 40.9% from 3.
Anthony, 37, entered into the league with LeBron James in the famed 2003 draft class, and the two have maintained a close friendship.
Anthony has earned more than $260 million in salary in his career and is a 10-time All-Star, six-time All-NBA selection and three-time Olympic gold medalist. Success has eluded him on the postseason stage, though. In 13 career playoff appearances, Anthony's teams have made the conference finals just once, and he has yet to play in the NBA Finals.
After being traded by the New York Knicks to the Oklahoma City Thunder in 2017, Anthony had an up-and-down season with the Thunder as the team failed to meet expectations. He was traded to the Atlanta Hawks the next offseason, then immediately waived.
He signed with the Rockets, agreeing to play a long-anticipated bench role for the contenders led by James Harden and Chris Paul, but was waived after just 10 games. Anthony wasn't signed by another team that season, casting doubt on the future of his NBA career.
But the Blazers offered a lifeline, and Anthony accepted the role and opportunity to contribute to a Western Conference playoff team. He started all 58 games his first season with Portland as it dealt with a series of injuries, but he came off the bench in 66 of his 69 appearances last season.
A surefire future Hall of Famer, Anthony currently sits at 27,370 points, just 39 points behind Moses Malone for ninth.
He won the scoring title with the Knicks in 2012-13, averaging 28.7 points. Anthony spent 10 consecutive seasons in the top 10 in scoring and finished as a runner-up for the scoring title twice in that stretch.
The Lakers also on Tuesday agreed with restricted free agent Talen Horton-Tucker on a three-year, $32 million deal to stay with the team, his agents, Klutch Sports CEO Rich Paul and Lucas Newton, told Wojnarowski.
Horton-Tucker is an important player for the Lakers -- a 20-year-old ascending talent with a penchant for scoring.
A second-round pick by L.A. in 2019, Horton-Tucker averaged 9.0 points on 45.8% shooting with 2.6 rebounds, 2.8 assists and 1.0 steals in more than 20 minutes per game last season.
Nunn agreed to a two-year deal with the Lakers that includes a player option, a source told Wojnarowski. Nunn turned down significantly more money to chase a title in Los Angeles, the source said.
Nunn, who turned 26 on Tuesday, followed up a strong rookie season with a solid second year in which he averaged 14.6 points, 3.2 rebounds and 2.6 assists per game for the Miami Heat.
Monk, 22, enjoyed a breakout fourth season with the Charlotte Hornets as he averaged 11.7 points per game and shot a career-high 40.1% from 3-point range last season.
The Hornets did not extend a qualifying offer to Monk, which made him a free agent.
Per Elias Sports Bureau, they have now added six players age 32 or older this offseason -- Anthony, Westbrook, Dwight Howard, Wayne Ellington, Trevor Ariza and Kent Bazemore -- the most in a single offseason in NBA history.
The Lakers currently have 12 players (including the free agent acquisitions), and their average age at the start of the regular season will be 31 years, 302 days old (or 31.83). Per Elias, without weighing for playing time, the oldest team in NBA history is the 1997-98 Knicks (31.76); the oldest team weighted for playing time is the 2000-01 Jazz (32.6).
ESPN's Royce Young, Nick Friedell and Tim Bontemps contributed to this report.