Daheley began her BBC career in 2007, with roles reading the news on 1Xtra and Radio 1 before she moved to Radio 2 to read the news for six years on Ball’s breakfast show.
Commenting on Daheley’s Instagram post on Tuesday, Ball said: “Love you Tina. Class act darling girl. I can highly recommend the later start to your day.”
Incoming breakfast host Cox wrote: “18 years, incredible, such a pro.”
Dermot O’Leary, who hosts a Saturday morning show on the station, wrote: “Congrats Tina, great shift x”.
Travel presenter Ellie Brennan described Daheley as “the most brilliant, hilarious friend” and said “We’re going to miss you so much in the mornings,” implying that she will remain on the breakfast show when Cox joins.
Channel 5 news presenter and former BBC Breakfast host Dan Walker, Radio 2’s DJ Spoony, and Ball’s breakfast show sidekicks Mike Williams and Richie Anderson were also among those who sent good wishes.
Radio 2’s Sean Keaveny wrote: “Ooh, imagine those extra hours in bed. Well deserved,” while rapper Wretch 32 described her tenure as a “superb innings” and screenwriter Russell T Davies simply posted three heart emojis.
Daheley also presents BBC television news bulletins and fronts BBC show Points of View.
Cox takes over the Radio 2 Breakfast Show on 6 July, with Toy Story 5 star Tom Hanks announced as her first guest.
She recently joked to fellow radio presenter Vernon Kay that she would be setting 42 alarm clocks to make sure she was up on time on the first day, adding: “I can’t wait – it’s so exciting.”