Dudley's agent, Mark Bartelstein, relayed the news to the reporter.
Dudley, who turns 34 on July 10, averaged 4.9 points and 2.6 rebounds on 42.3 percent shooting for the Brooklyn Nets last season. He started 25 of his 59 contests.
The 6'7" forward has played 12 NBA seasons for six teams after he was picked 22nd overall out of Boston College in the 2007 draft.
With LeBron James and Anthony Davis co-leading the team, the Lakers, barring injury, figure to make a deep playoff run. Los Angeles is a +140 favorite ($100 bet to win $140) to win it all in 2019-20, per Caesars Palace.
However, L.A. must round out a roster that saw numerous members of last year's core (plus a multitude of draft picks) head to the New Orleans Pelicans in the Davis deal.
Adding veterans on one-year deals is a clear route. Dudley may not be a flashy player or one who figures to be in L.A. long-term, but he's the type of steady veteran who can help round out the rotation and provide solid minutes off the bench when called upon. He was an excellent fit last season on a surprising Nets team that finished 42-40 and landed sixth in the Eastern Conference after going just 28-54 the year before.
Dudley joins another veteran in Troy Daniels, who also signed on a cheap one-year deal, per Shams Charania of Stadium and The Athletic. Daniels scored 6.2 points per game while shooting 41.1 percent from the field and 38.1 percent from three-point range for the Phoenix Suns last season.