Gallagher, who joined Palace on loan from Chelsea in summer, has played 27 games for the south Londoners so far, scoring eight and assisting five.
The London Football Awards (LFA) celebrates the very best in London football, and is an annual event in support of the Willow Foundation, the only national charity that helps provide special occasions for seriously ill young adults aged 16 to 40 years old when they are needed most.
Gallagher joined Tyrick Mitchell as a nominee for Young Player of the Year, and pipped his teammate and Fabio Carvalho, Bukayo Saka and Oliver Skipp, to the award.
He was also nominated for Goal of the Season after his strike against Brighton & Hove Albion, and Patrick Vieira was in the running for Manager of the Season.
This award follows a nomination for the Premier League's February Goal of the Month.
Gallagher collected his trophy at a ceremony in north London, and told cpfc.co.uk: "I’m delighted to get this award. It's a very proud moment for me and my family; it means a lot.
"I’ve got to give a lot of credit to Crystal Palace. They’ve given me the confidence and platform to show people what I can do the best way possible. I’ve got to thank them for that, because I don’t think this would be possible without being able to do that here. I’m just really pleased and happy and thankful to receive this award."