Having left Manchester City in search of first-team football, Palmer has relished the senior role that he has been given by Mauricio Pochettino.
A total of 24 goals and 13 assists have been recorded in all competitions, 30 of those contributions coming in the Premier League.
Palmer will be in the running for numerous awards over the coming weeks, albeit with the Premier League's top goalscorer now realistically out of his grasp after Erling Haaland's four-goal haul against Wolverhampton Wanderers at the weekend.
Nevertheless, the 22-year-old's efforts were rewarded on Tuesday evening as Chelsea held their awards night for the 2023-24 campaign.
Palmer collects two accolades
Palmer was first presented with the Men's Players' Player Of The Year trophy, as voted for by the men's first-team squad.
His second accolade was the Men's Player Of The Year award, as voted for by the club's supporters.
Speaking to those who attended the evening, Palmer said: "It's been a dream debut season for me. Thank you to the manager, staff, players and, of course, the fans.
"I just came to play to showcase my abilities and talent to the fans. It's gone amazing, probably better than I'd imagined. Buzzing."
The England international also disclosed his own vote, revealing that he had gone with the choice of right-back Malo Gusto.
He added: "I voted for Malo Gusto. I love playing with him on the right. He's been amazing this season when he's played as well."
Gusto has made 34 appearances during his first season at Stamford Bridge, contributing eight assists from the flank in the absence of Reece James.
Who else won awards?
The other major men's award went to Alfie Gilchrist, who was rewarded with the Academy Player Of The Year accolade having made the breakthrough into the senior ranks with five starts and 12 substitute outings.
Jessica Carter lifted the Women's Players' Player Of The Year trophy having starred in defence, both in the WSL where she has missed just one game and the Champions League.
Lauren James was the recipient of the Women's Player Of The Year award, voted by the supporters, for her 16 goals in all competitions.