Reggie, who is leaving to concentrate on his TV work, is joined by Vernon Kay who also announced his departure.
Vernon - the husband of Strictly Come Dancing presenter Tess Daly, with whom he has two daughters - said: "I've had an incredible nine and a half years at Radio 1 that has exceeded all of my expectations, it has been a fabulous experience and I've loved the weekends I have spent with my listeners.
"However, when I was offered a contract extension I thought long and hard, but after 12 years of working weekends with CBBC, T4 and Radio 1, I felt it was the right time to leave as the girls are now both in school so weekends are more precious than ever."
Jameela, who will take over when Reggie leaves at the end of the year, said: "I am absolutely delighted and honoured. I'm fully aware that I have big shoes to fill and am so excited to get started. I've grown up listening to the official chart so I cannot thank Radio 1 enough for the amazing opportunity."
Reggie, who has presented the show for five years, said: "I have absolutely loved my time hosting the Chart Show. It's been a privilege to deliver to the nation the weekly No 1 song, but after 10 years at Radio 1/1Xtra I am looking forward to focusing on other projects and new challenges."
Radio 1 controller Ben Cooper said: "I'd like to thank Vernon and Reggie who have both been excellent ambassadors for Radio 1 and Radio 1Xtra during their ten years with us. I wish them all the very best."