It was one of the most painfully symbolic transactions in Lakers' history.
Nash, 41, announced his intention to retire last week but had remained on the Lakers' roster and would still receive his entire $9.7-million salary despite being waived.
Brown scored 22 points Monday against Philadelphia in what could have been his final game with the Lakers. His second 10-day contract expired that night, and the team had to decide whether to let him walk or sign him for the final two weeks of the season.
The Lakers also gave him a nonguaranteed contract for next season for about $900,000. He will make just under $50,000 from now until April 15.
"Every game it seems like he shows you a little bit something else," Lakers Coach Byron Scott said. "He seems a little bit more confident, a little bit more comfortable every game."
Brown, 22, was averaging 9.4 points in 10 games since the Lakers plucked him from their Development League affiliate, the L.A. D-Fenders. He played college basketball at Missouri with Lakers rookie Jordan Clarkson.
Brown said after Monday's game he felt as if "he helped himself" after making seven of 10 shots, three of four from three-point range, in the Lakers' 111-109 overtime victory.
He was cut by the Lakers after training camp last October because he wasn't aggressive enough, seemingly tentative to shoot or drive. That hasn't been a problem this time. He's a shooting guard by nature but added some ball-handling responsibilities because of the Lakers' lack of point guards in recent games.
"I wanted to be aggressive, but I didn't want to force, take bad shots, stuff like that," Brown said. "I felt like I was showing I could do a lot of things out there on the court."
Brown was undrafted out of college but made some noise with the D-Fenders, averaging 24.4 points in the high-scoring Development League. He was shooting a strong 50% overall with the Lakers and 45.8% from three-point range going into Wednesday's game against New Orleans.
"I felt like I played well enough. I just know sometimes other things go into it," Brown said. "So I was just hoping for the best."
Nash played in 65 games for the Lakers, unable to overcome a slew of injuries that included recurring back problems and, in only his second game with the team, a broken leg. He did not play a game this season after announcing his decision to sit out because of his back.
He did not formally announce his retirement until last week, giving the Lakers the chance to try to trade his expiring contract. It was only a matter of time for Nash's retirement announcement once the trade deadline came and went in late February.
Times correspondent Eric Pincus contributed to this report.