"It's a great organization, a franchise with a lot of history here," said Davis. "I think it's an opportunity where I can play and help this team win."
The 25-year-old, four-year veteran likely will earn the NBA minimum of $981,084 this season with a player option on a second year at $1.1 million.
"He has a very promising future. He's going to continue to work and develop in this league," said General Manager Mitch Kupchak, who left without answering questions -- like about the team's protracted coaching vacancy -- after welcoming Davis.
Former Coach Mike D'Antoni resigned at the end of April. The Lakers are the only NBA franchise currently without a head coach.
It remains unclear how exactly Davis will fit into the Lakers' forward-heavy rotation, with rookie power forward Julius Randle, returning forward Ryan Kelly and recently acquired veteran power forward Carlos Boozer.
"It's tough to say that without a coach," said Davis.
"I can play both positions, the four and the five," said the 6-foot-10 Davis. "I bring athleticism, defend, run the floor, block shots, rebound -- all the little things."
Davis will wear No. 21 with the team, Kupchak's number when he was in college at North Carolina.
The Lakers now have two players from rival Duke -- Kelly and Boozer -- and while Davis is a Tar Heel, the team recently cut North Carolina point guard Kendall Marshall.
Davis was originally drafted by the Toronto Raptors in 2010 with the 13th overall pick. He was traded in January 2013 to the Memphis Grizzlies for Rudy Gay. Davis fell behind Zach Randolph and Marc Gasol in the rotation.
"It definitely was a challenge, but just took it as a learning experience," he said. "Playing behind Z and Marc, they're such good players, just learning from them every night just helped me out."
Last season, Davis averaged 5.7 points and 4.1 rebounds through 63 appearances, playing just 15.2 minutes a game. Given 24.2 minutes a night in Toronto before the trade, Davis contributed 9.7 points with 6.7 rebounds.
Davis will wear 21 with the Lakers, Ronny Turiaf's former number.
"I wanted 32 but it's gone. It was my number in high school, my ninth grade year," said Davis of No. 21. "Another reason I had 21 was because of Kevin Garnett. I watched him growing up. He was my favorite player back in the day."
Magic Johnson's No. 32 has been retired by the Lakers.
Davis is already established in Los Angeles, with a place in the Marina del Rey. He'll be working out regularly at the Lakers' practice facility in El Segundo.
"I talked to Kobe on the phone," said Davis, who chose not to elaborate on his conversation with the Lakers' All-Star guard. "I'll keep it private."