Steve Nash logged his first assist as a Laker more than three months before the season opener.
"Jordan was excited about the fact that Steve Nash decided to join the Lakers and the prospect of winning a championship in L.A.," said Kevin Bradbury, Hill's agent.
Hill will further fortify the Lakers' bench after forward Antawn Jamison agreed this week to a one-year deal for the veteran's minimum of $1.4 million.
The Lakers acquired the 6-foot-10 Hill in March at the trading deadline in what amounted to a salary dump involving Derek Fisher and a first-round draft pick that was also sent to the Houston Rockets.
Hill, who turns 25 this week, became an unrestricted free agent when Houston decided not to pick up his $3.6-million option for next season before trading him to the Lakers.
Hill was also courted by the Minnesota Timberwolves, but Bradbury said Lakers General Manager Mitch Kupchak's willingness to bring Hill to Los Angeles and give him an opportunity in the playoffs was a factor in his decision to return.
The former lottery pick was a force late in the regular season and during the Lakers' first-round playoff series against Denver, with three double-doubles in a six-game span, before fading in the Western Conference semifinals against Oklahoma City. He averaged 3.8 points and 5.0 rebounds in that series against the Thunder.
Overall, Hill averaged 4.7 points and 4.4 rebounds in seven regular-season games with the Lakers before those averages increased to 4.8 points and 6.3 rebounds in the playoffs.
Hill has an uncertain legal future. He faces third-degree felony charges for allegedly choking his girlfriend in February in Houston. Hill could spend up to 10 years in prison if convicted.
"He feels like he didn't do anything wrong," Hill's attorney, Rusty Hardin Jr., recently told The Times. "He wants to get it behind him."