Andersen was kicked out of the NBA on Jan. 27, 2006, for violating the league's drug policy.
"A lot of people, when they fail, they stay there ... but the strong person always rises up after making a mistake or failing, and you have done just that," Hornets owner George Shinn told Andersen. "You will shine again and we are very happy to have you here."
The NBA reinstated him on Tuesday, when Andersen was in New Orleans for a physical.
Andersen's rights belonged to the Hornets as long as they offered him a contract within 30 days. The free-agent contract was announced on Wednesday, but the terms were not disclosed.
Wearing official Hornets practice gear, Andersen smiled and thanked the Hornets for supporting his comeback, which acquired a more official air moments later when he joined a game-day shootaround. He ran the floor with a pair of teammates in a three-man weave.
"It has been a long journey and I have learned patience over the last two years," Andersen said. "I'm not here to step on anybody's toes. I'm here to make players better. I know I'm not going to come in and play a lot of minutes. I wasn't expecting that."
He then glanced over at Hornets coach Byron Scott and said, "I love B-Scott. It's good to be playing for him again. ... I'm just really glad to be here."
Scott had fond words for his returning 6-foot-10 reserve, although he was unsure how long he would wait before playing Andersen. His first chance is Wednesday night, when the Hornets play host to Atlanta.
"It's no secret that Bird was one of my favorites because of his athleticism, his joy for the game, his enthusiasm. He was terrific on the court as well as off the court," Scott said. "Being out of the league for a couple of seasons -- sometimes, when that happens, guys don't fight enough to get back and I'm very proud of Bird that he was able to get back to this level."
However, Scott later said Andersen would have to earn the trust of his teammates and prove himself in practice before he plays again.
"I'm trying to win basketball games. That's the bottom line," Scott said. "I'm not putting guys out there for sympathy, ticket sales ... When it comes playoff time, the guys that are playing the best and the guys I feel most comfortable with are the guys who'll be on the roster."
Neither the NBA nor the players' union is allowed to comment on the specifics of a drug test, but according to the collective bargaining agreement, a player can only be disqualified for a fourth positive test for performance-enhancing drugs, or a first positive test for "drugs of abuse."
Andersen has not previously been suspended for testing positive for performance-enhancing drugs. The drugs on the "drugs of abuse" list are amphetamine and its analogs, which include methamphetamine; cocaine; LSD; opiates, including heroin, codeine and morphine; and PCP.
Andersen was a fan-favorite in New Orleans during the Hornets' last season here before Hurricane Katrina displaced the club to Oklahoma City for two seasons. He averaged 5.1 points, 4.8 rebounds and 1.3 blocks during a little more than four seasons in the NBA before becoming the first player thrown out for drugs since Stanley Roberts in 1999.
He played three seasons in Denver before joining New Orleans for the 2004-05 season.
During his suspension, Andersen said he worked out constantly with a trainer in Denver or Las Vegas, often spending six hours or more in the gym.
He had a twinkle in his eye as he tried to explain what had changed about him -- and what had not -- during his road back to pro basketball.
"I'm still crazy. I'm still going to do the wild things on the court and everything," Andersen said, adding he was smarter and more mature in handling personal matters. "You tend to grow up a lot in a situation like that over the past two years."